bibkey: cloitre2004a090825 authors: Benoit Cloitre year: 2004 title: “OEIS A090825, nonprimes n such that (3/2)(1/n)(2n+1)(3^n+1)B(2n) is an integer” doi: null url: https://oeis.org/A090825 claim: “A090825 %N: Nonprimes n such that (3/2)(1/n)(2n+1)(3^n+1)B(2n) is an integer, where B(k) denotes the k-th Bernoulli number. A090825 %C: Conjecture: composite numbers with all prime factors in A053176 are in the sequence. - Benoit Cloitre, Feb 11 2004” strata_touched:

• D5/S3/Arith/Congruence/CloitreBernoulliIntegralityRefutation license: citation-only triage: anchor

OEIS A090825

The NAME of A090825 states:

Nonprimes n such that (3/2)(1/n)(2n+1)(3^n+1)B(2n) is an integer, where B(k) denotes the k-th Bernoulli number.

Benoit Cloitre’s COMMENT of February 11, 2004 states:

Conjecture: composite numbers with all prime factors in A053176 are in the sequence.

The AUTHOR line is:

Benoit Cloitre, Feb 11 2004

Verified locator

• URL: https://oeis.org/A090825
• NAME (verbatim): Nonprimes n such that (3/2)(1/n)(2n+1)(3^n+1)B(2n) is an integer, where B(k) denotes the k-th Bernoulli number.
• COMMENT (verbatim): Conjecture: composite numbers with all prime factors in A053176 are in the sequence.

Only the conjecture about composites whose prime factors all lie in A053176 is refuted: 833 satisfies its premise, but the von Staudt-Clausen theorem gives F(833) a denominator of 239. The second COMMENT clause about primes and the question concerning the subsequence beginning 91, 247 are untouched.