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

1,1

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

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

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 *)

Crossrefs

Cf. A000330, A001044.

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

Sequence in context: A144426 A233518 A118942 * A166602 A079697 A079695

Adjacent sequences: A067653 A067654 A067655 * A067657 A067658 A067659

Keyword

nonn

Author

Benoit Cloitre, Feb 03 2002

Status

approved