A045979 Bernoulli number B_{2n} has denominator 6.

1, 7, 13, 17, 19, 31, 37, 43, 47, 49, 59, 61, 67, 71, 73, 79, 91, 97, 101, 103, 107, 109, 127, 133, 137, 139, 149, 151, 157, 163, 167, 169, 181, 193, 197, 199, 211, 217, 223, 227, 229, 241, 247, 257, 259, 263, 269, 271, 277, 283, 289

Offset

1,2

Comments

All primes in A053176 are in the sequence. If n is in the sequence, its factorization contains only primes in A053176. - Benoit Cloitre, Oct 19 2002

B(2n) has denominator 6 iff (n^2-1)*B(2n) is an integer. - Benoit Cloitre, Feb 15 2004

Subsequence of A156543. - Reinhard Zumkeller, Feb 10 2009

References

B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 76.

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Index entries for sequences related to Bernoulli numbers.

Formula

a(n) seems to be asymptotic to c*n, 5 < c < 6. - Benoit Cloitre, Oct 19 2002

Mathematica

ok[n_] := IntegerQ[(n^2 - 1)*BernoulliB[2n]]; Select[Range[300], ok] (* Jean-François Alcover, Jun 27 2012, after Benoit Cloitre *)
result = {}; Do[count = 0;
Do[If[Not[PrimeQ[2*Divisors[n][[i]] + 1]], count++],
{i, 2, DivisorSigma[0, n]}]; If[count == DivisorSigma[0, n] - 1, AppendTo[result, n]], {n, 1, 10000}]; result  (* Richard R. Forberg, Aug 06 2016 *)
Position[BernoulliB[2 Range[300]], _?(Denominator[#]==6&)]//Flatten (* Harvey P. Dale, Jan 28 2017 *)

Prog

(PARI) isok(n) = denominator(bernfrac(2*n)) == 6; \\ Michel Marcus, Feb 06 2016
(Magma) [n: n in [0..400] | Denominator(Bernoulli(2*n)) eq 6]; // Vincenzo Librandi, Feb 06 2016

Crossrefs

Cf. A051222, A053176, A156543.

Sequence in context: A097959 A156543 A090863 * A079699 A053176 A032669

Adjacent sequences: A045976 A045977 A045978 * A045980 A045981 A045982

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Status

approved