A067656 Numbers n such that n!*B(2n) is an integer, where B(2n) are the Bernoulli numbers.

7, 13, 17, 19, 24, 25, 27, 31, 32, 34, 37, 38, 43, 45, 47, 49, 55, 57, 59, 61, 62, 64, 67, 71, 73, 76, 77, 79, 80, 84, 85, 87, 91, 92, 93, 94, 97, 101, 103, 104, 107, 109, 110, 115, 117, 118, 121, 122, 123, 124, 127, 129, 132, 133, 137, 139, 142, 143, 144, 145, 147

Offset: 1

Author

Benoit Cloitre, Feb 03 2002

Keywords

• nonn

Comments

A045979(n), Bernoulli numbers with denominators 6, are included in the sequence.

Also numbers n such that both n+1 and 2n+1 are not prime. - Alexander Adamchuk, Oct 05 2006

Links

• Alexander Adamchuk, Oct 05 2006, Table of n, a(n) for n = 1..565

Crossrefs

Cf. A000330, A001044.

Cf. A166602. - R. J. Mathar, Feb 14 2010

Programs

Mathematica

Select[Range[2,1000],Numerator[ #(#+1)(2#+1)/6/#!^2]==1&] (* Alexander Adamchuk, Oct 05 2006 *)
Select[Range[1000],!PrimeQ[ #+1]&&!PrimeQ[2#+1]&] (* Alexander Adamchuk, Oct 05 2006 *)

Formula

Also numbers n>1 such that A000330[n] = Sum[k^2,{k,1,n}] = n(n+1)(2n+1)/6 divides A001044[n] = Product[k^2,{k,1,n}] = (n!)^2. Also numbers n>1 such that Numerator[n(n+1)(2n+1)/6 /(n!)^2] = 1. - Alexander Adamchuk, Oct 05 2006