本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。
本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。
batch-20261014-advance-20261109-r06-mobius-function-foundations · 2026-10-14 · 100 題
欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":2}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(2, [2], [2], -1, squarefree_parity_sign)
Wave6第三層核對=(2, [2], [2], -1, squarefree_parity_sign)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":6}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(6, [2, 3], [2, 3], 1, squarefree_parity_sign)
Wave6第三層核對=(6, [2, 3], [2, 3], 1, squarefree_parity_sign)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":12}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(12, [2, 2, 3], [2, 3], 0, square_prime_factor_gives_zero)
Wave6第三層核對=(12, [2, 2, 3], [2, 3], 0, square_prime_factor_gives_zero)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":20}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(20, [2, 2, 5], [2, 5], 0, square_prime_factor_gives_zero)
Wave6第三層核對=(20, [2, 2, 5], [2, 5], 0, square_prime_factor_gives_zero)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":30}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(30, [2, 3, 5], [2, 3, 5], -1, squarefree_parity_sign)
Wave6第三層核對=(30, [2, 3, 5], [2, 3, 5], -1, squarefree_parity_sign)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":42}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(42, [2, 3, 7], [2, 3, 7], -1, squarefree_parity_sign)
Wave6第三層核對=(42, [2, 3, 7], [2, 3, 7], -1, squarefree_parity_sign)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":56}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(56, [2, 2, 2, 7], [2, 7], 0, square_prime_factor_gives_zero)
Wave6第三層核對=(56, [2, 2, 2, 7], [2, 7], 0, square_prime_factor_gives_zero)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":72}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(72, [2, 2, 2, 3, 3], [2, 3], 0, square_prime_factor_gives_zero)
Wave6第三層核對=(72, [2, 2, 2, 3, 3], [2, 3], 0, square_prime_factor_gives_zero)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":90}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(90, [2, 3, 3, 5], [2, 3, 5], 0, square_prime_factor_gives_zero)
Wave6第三層核對=(90, [2, 3, 3, 5], [2, 3, 5], 0, square_prime_factor_gives_zero)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":110}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(110, [2, 5, 11], [2, 5, 11], -1, squarefree_parity_sign)
Wave6第三層核對=(110, [2, 5, 11], [2, 5, 11], -1, squarefree_parity_sign)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":132}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(132, [2, 2, 3, 11], [2, 3, 11], 0, square_prime_factor_gives_zero)
Wave6第三層核對=(132, [2, 2, 3, 11], [2, 3, 11], 0, square_prime_factor_gives_zero)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":156}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(156, [2, 2, 3, 13], [2, 3, 13], 0, square_prime_factor_gives_zero)
Wave6第三層核對=(156, [2, 2, 3, 13], [2, 3, 13], 0, square_prime_factor_gives_zero)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":182}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(182, [2, 7, 13], [2, 7, 13], -1, squarefree_parity_sign)
Wave6第三層核對=(182, [2, 7, 13], [2, 7, 13], -1, squarefree_parity_sign)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":210}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(210, [2, 3, 5, 7], [2, 3, 5, 7], 1, squarefree_parity_sign)
Wave6第三層核對=(210, [2, 3, 5, 7], [2, 3, 5, 7], 1, squarefree_parity_sign)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":240}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(240, [2, 2, 2, 2, 3, 5], [2, 3, 5], 0, square_prime_factor_gives_zero)
Wave6第三層核對=(240, [2, 2, 2, 2, 3, 5], [2, 3, 5], 0, square_prime_factor_gives_zero)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":272}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(272, [2, 2, 2, 2, 17], [2, 17], 0, square_prime_factor_gives_zero)
Wave6第三層核對=(272, [2, 2, 2, 2, 17], [2, 17], 0, square_prime_factor_gives_zero)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":306}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(306, [2, 3, 3, 17], [2, 3, 17], 0, square_prime_factor_gives_zero)
Wave6第三層核對=(306, [2, 3, 3, 17], [2, 3, 17], 0, square_prime_factor_gives_zero)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":342}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(342, [2, 3, 3, 19], [2, 3, 19], 0, square_prime_factor_gives_zero)
Wave6第三層核對=(342, [2, 3, 3, 19], [2, 3, 19], 0, square_prime_factor_gives_zero)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":380}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(380, [2, 2, 5, 19], [2, 5, 19], 0, square_prime_factor_gives_zero)
Wave6第三層核對=(380, [2, 2, 5, 19], [2, 5, 19], 0, square_prime_factor_gives_zero)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":420}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(420, [2, 2, 3, 5, 7], [2, 3, 5, 7], 0, square_prime_factor_gives_zero)
Wave6第三層核對=(420, [2, 2, 3, 5, 7], [2, 3, 5, 7], 0, square_prime_factor_gives_zero)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":462}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(462, [2, 3, 7, 11], [2, 3, 7, 11], 1, squarefree_parity_sign)
Wave6第三層核對=(462, [2, 3, 7, 11], [2, 3, 7, 11], 1, squarefree_parity_sign)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":506}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(506, [2, 11, 23], [2, 11, 23], -1, squarefree_parity_sign)
Wave6第三層核對=(506, [2, 11, 23], [2, 11, 23], -1, squarefree_parity_sign)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":552}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(552, [2, 2, 2, 3, 23], [2, 3, 23], 0, square_prime_factor_gives_zero)
Wave6第三層核對=(552, [2, 2, 2, 3, 23], [2, 3, 23], 0, square_prime_factor_gives_zero)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":600}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(600, [2, 2, 2, 3, 5, 5], [2, 3, 5], 0, square_prime_factor_gives_zero)
Wave6第三層核對=(600, [2, 2, 2, 3, 5, 5], [2, 3, 5], 0, square_prime_factor_gives_zero)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-canonical-value；資料={"n":650}。請依 [n, prime_multiset, distinct_primes, mu, certificate] 欄序回答。
(650, [2, 5, 5, 13], [2, 5, 13], 0, square_prime_factor_gives_zero)
Wave6第三層核對=(650, [2, 5, 5, 13], [2, 5, 13], 0, square_prime_factor_gives_zero)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-canonical-value · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":4,"factors":[2,2]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(4, [2, 2], 是, 0, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(4, [2, 2], 是, 0, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":6,"factors":[2,3]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(6, [2, 3], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(6, [2, 3], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":10,"factors":[2,5]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(10, [2, 5], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(10, [2, 5], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":14,"factors":[2,7]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(14, [2, 7], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(14, [2, 7], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":22,"factors":[2,11]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(22, [2, 11], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(22, [2, 11], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":26,"factors":[2,13]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(26, [2, 13], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(26, [2, 13], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":34,"factors":[2,17]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(34, [2, 17], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(34, [2, 17], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":38,"factors":[2,19]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(38, [2, 19], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(38, [2, 19], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":46,"factors":[2,23]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(46, [2, 23], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(46, [2, 23], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":58,"factors":[2,29]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(58, [2, 29], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(58, [2, 29], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":62,"factors":[2,31]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(62, [2, 31], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(62, [2, 31], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":74,"factors":[2,37]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(74, [2, 37], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(74, [2, 37], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":82,"factors":[2,41]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(82, [2, 41], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(82, [2, 41], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":86,"factors":[2,43]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(86, [2, 43], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(86, [2, 43], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":94,"factors":[2,47]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(94, [2, 47], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(94, [2, 47], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":106,"factors":[2,53]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(106, [2, 53], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(106, [2, 53], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":118,"factors":[2,59]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(118, [2, 59], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(118, [2, 59], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":122,"factors":[2,61]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(122, [2, 61], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(122, [2, 61], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":134,"factors":[2,67]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(134, [2, 67], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(134, [2, 67], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":142,"factors":[2,71]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(142, [2, 71], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(142, [2, 71], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":146,"factors":[2,73]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(146, [2, 73], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(146, [2, 73], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":158,"factors":[2,79]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(158, [2, 79], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(158, [2, 79], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":166,"factors":[2,83]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(166, [2, 83], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(166, [2, 83], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":178,"factors":[2,89]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(178, [2, 89], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(178, [2, 89], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-factorization-audit；資料={"n":194,"factors":[2,97]}。請依 [n, factors, valid_prime_product, mu_or_null, agrees_with_canonical, certificate] 欄序回答。
(194, [2, 97], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)
Wave6第三層核對=(194, [2, 97], 是, 1, 是, complete_UPF_multiplicity_and_distinct_prime_count)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-factorization-audit · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":1}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(1, [[1, 1]], 1, 1, 是)
Wave6第三層核對=(1, [[1, 1]], 1, 1, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":2}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(2, [[1, 1], [2, -1]], 0, 0, 是)
Wave6第三層核對=(2, [[1, 1], [2, -1]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":3}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(3, [[1, 1], [3, -1]], 0, 0, 是)
Wave6第三層核對=(3, [[1, 1], [3, -1]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":4}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(4, [[1, 1], [2, -1], [4, 0]], 0, 0, 是)
Wave6第三層核對=(4, [[1, 1], [2, -1], [4, 0]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":5}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(5, [[1, 1], [5, -1]], 0, 0, 是)
Wave6第三層核對=(5, [[1, 1], [5, -1]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":6}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(6, [[1, 1], [2, -1], [3, -1], [6, 1]], 0, 0, 是)
Wave6第三層核對=(6, [[1, 1], [2, -1], [3, -1], [6, 1]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":7}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(7, [[1, 1], [7, -1]], 0, 0, 是)
Wave6第三層核對=(7, [[1, 1], [7, -1]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":8}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(8, [[1, 1], [2, -1], [4, 0], [8, 0]], 0, 0, 是)
Wave6第三層核對=(8, [[1, 1], [2, -1], [4, 0], [8, 0]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":9}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(9, [[1, 1], [3, -1], [9, 0]], 0, 0, 是)
Wave6第三層核對=(9, [[1, 1], [3, -1], [9, 0]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":10}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(10, [[1, 1], [2, -1], [5, -1], [10, 1]], 0, 0, 是)
Wave6第三層核對=(10, [[1, 1], [2, -1], [5, -1], [10, 1]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":11}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(11, [[1, 1], [11, -1]], 0, 0, 是)
Wave6第三層核對=(11, [[1, 1], [11, -1]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":12}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(12, [[1, 1], [2, -1], [3, -1], [4, 0], [6, 1], [12, 0]], 0, 0, 是)
Wave6第三層核對=(12, [[1, 1], [2, -1], [3, -1], [4, 0], [6, 1], [12, 0]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":13}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(13, [[1, 1], [13, -1]], 0, 0, 是)
Wave6第三層核對=(13, [[1, 1], [13, -1]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":14}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(14, [[1, 1], [2, -1], [7, -1], [14, 1]], 0, 0, 是)
Wave6第三層核對=(14, [[1, 1], [2, -1], [7, -1], [14, 1]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":15}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(15, [[1, 1], [3, -1], [5, -1], [15, 1]], 0, 0, 是)
Wave6第三層核對=(15, [[1, 1], [3, -1], [5, -1], [15, 1]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":16}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(16, [[1, 1], [2, -1], [4, 0], [8, 0], [16, 0]], 0, 0, 是)
Wave6第三層核對=(16, [[1, 1], [2, -1], [4, 0], [8, 0], [16, 0]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":17}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(17, [[1, 1], [17, -1]], 0, 0, 是)
Wave6第三層核對=(17, [[1, 1], [17, -1]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":18}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(18, [[1, 1], [2, -1], [3, -1], [6, 1], [9, 0], [18, 0]], 0, 0, 是)
Wave6第三層核對=(18, [[1, 1], [2, -1], [3, -1], [6, 1], [9, 0], [18, 0]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":19}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(19, [[1, 1], [19, -1]], 0, 0, 是)
Wave6第三層核對=(19, [[1, 1], [19, -1]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":20}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(20, [[1, 1], [2, -1], [4, 0], [5, -1], [10, 1], [20, 0]], 0, 0, 是)
Wave6第三層核對=(20, [[1, 1], [2, -1], [4, 0], [5, -1], [10, 1], [20, 0]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":21}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(21, [[1, 1], [3, -1], [7, -1], [21, 1]], 0, 0, 是)
Wave6第三層核對=(21, [[1, 1], [3, -1], [7, -1], [21, 1]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":22}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(22, [[1, 1], [2, -1], [11, -1], [22, 1]], 0, 0, 是)
Wave6第三層核對=(22, [[1, 1], [2, -1], [11, -1], [22, 1]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":23}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(23, [[1, 1], [23, -1]], 0, 0, 是)
Wave6第三層核對=(23, [[1, 1], [23, -1]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":24}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(24, [[1, 1], [2, -1], [3, -1], [4, 0], [6, 1], [8, 0], [12, 0], [24, 0]], 0, 0, 是)
Wave6第三層核對=(24, [[1, 1], [2, -1], [3, -1], [4, 0], [6, 1], [8, 0], [12, 0], [24, 0]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-divisor-sum；資料={"n":25}。請依 [n, divisor_mu_rows, sum, target, equal] 欄序回答。
(25, [[1, 1], [5, -1], [25, 0]], 0, 0, 是)
Wave6第三層核對=(25, [[1, 1], [5, -1], [25, 0]], 0, 0, 是)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-divisor-sum · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":0}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(0, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(0, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-1}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-1, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-1, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-2}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-2, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-2, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-3}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-3, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-3, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-4}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-4, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-4, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-5}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-5, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-5, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-6}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-6, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-6, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-7}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-7, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-7, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-8}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-8, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-8, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-9}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-9, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-9, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-10}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-10, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-10, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-11}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-11, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-11, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-12}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-12, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-12, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-13}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-13, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-13, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-14}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-14, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-14, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-15}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-15, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-15, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-16}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-16, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-16, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-17}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-17, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-17, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-18}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-18, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-18, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-19}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-19, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-19, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-20}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-20, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-20, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-21}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-21, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-21, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-22}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-22, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-22, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-23}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-23, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-23, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate
positive integer domain與完整UPF multiplicities。操作=mobius-domain-boundary；資料={"n":-24}。請依 [n, in_positive_domain, mu_or_null, boundary] 欄序回答。
(-24, 否, null, Mobius_domain_positive_integers_only)
Wave6第三層核對=(-24, 否, null, Mobius_domain_positive_integers_only)；依完整明示資料獨立重算；mu(1)=1，square prime factor gives0，squarefree sign由distinct prime count parity；factor order不影響；zero negative或incomplete trial result不可分類。
Möbius函數 · qf-mod40-mobius-domain-boundary · candidate