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Numbers n such that n!*B(2n) is an integer, where B(2n) are the Bernoulli numbers.
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%I #13 Mar 08 2015 18:04:34

%S 7,13,17,19,24,25,27,31,32,34,37,38,43,45,47,49,55,57,59,61,62,64,67,

%T 71,73,76,77,79,80,84,85,87,91,92,93,94,97,101,103,104,107,109,110,

%U 115,117,118,121,122,123,124,127,129,132,133,137,139,142,143,144,145,147

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

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

%C Also numbers n such that both n+1 and 2n+1 are not prime. - _Alexander Adamchuk_, Oct 05 2006

%H Alexander Adamchuk, Oct 05 2006, <a href="/A067656/b067656.txt">Table of n, a(n) for n = 1..565</a>

%F 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

%t Select[Range[2,1000],Numerator[ #(#+1)(2#+1)/6/#!^2]==1&] (* _Alexander Adamchuk_, Oct 05 2006 *)

%t Select[Range[1000],!PrimeQ[ #+1]&&!PrimeQ[2#+1]&] (* _Alexander Adamchuk_, Oct 05 2006 *)

%Y Cf. A000330, A001044.

%Y Cf. A166602. - _R. J. Mathar_, Feb 14 2010

%K nonn

%O 1,1

%A _Benoit Cloitre_, Feb 03 2002