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

Author

Benoit Cloitre, Jun 21 2003

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..5530
• Wikipedia, Bernoulli numbers.

Crossrefs

Cf. A000367.

Programs

Mathematica

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

PARI

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

Extensions

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