A084217 Number of k's 1 <= k <= n dividing the numerator of 2n-th Bernoulli number.

1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 3, 2, 1, 2, 2, 1, 2, 1, 2, 2, 4, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 3, 1, 2, 3, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 1, 4, 2, 2, 2, 2, 3, 2, 1, 2, 2, 3, 2, 4, 1, 2, 2, 1, 2, 2, 1, 4, 2, 2, 3, 2, 1, 4, 2, 2, 2, 5, 1, 2, 3, 2, 1, 2, 2, 2, 2, 2

Offset

1,5

Links

Antti Karttunen, Table of n, a(n) for n = 1..5530

Wikipedia, Bernoulli numbers.

Mathematica

a[n_] := Count[Range[n], _?(Divisible[Numerator[BernoulliB[2*n]], #] &)]; Array[a, 100] (* Amiram Eldar, Apr 27 2025 *)

Prog

(PARI) a(n)=sum(k=1, n, if(numerator(bernfrac(2*n))%k, 0, 1))

Crossrefs

Cf. A000367.

Sequence in context: A227945 A003647 A353352 * A381587 A245548 A025903

Adjacent sequences: A084214 A084215 A084216 * A084218 A084219 A084220

Keyword

nonn

Author

Benoit Cloitre, Jun 21 2003

Extensions

Missing a(1)=1 inserted and data section extended to a(105) by Antti Karttunen, Jan 19 2025

Status

approved