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%I #24 Aug 20 2021 22:49:18
%S 1,5,7,11,13,17,19,23,25,29,31,35,37,41,43,47,49,53,59,61,65,67,71,73,
%T 77,79,83,85,89,91,95,97,101,103,107,109,113,115,119,121,125,127,131,
%U 133,137,139,143,145,149,151,155,157,161,163,167,169,173,175,179,181
%N Numbers k that divide the numerator of B(2k) (the Bernoulli numbers).
%C Equivalently, k is relatively prime to the denominator of B(2k). Equivalently, there are no primes p such that p divides k and p-1 divides 2k. These equivalences follow from the von Staudt-Clausen and Sylvester-Lipschitz theorems.
%C The listed terms are the same as those in A070191, but the sequences are not identical. (The similarity is mostly explained by the absence of multiples of 2, 3 and 55 from both sequences.) See A070192 and A070193 for the differences.
%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 3rd ed., Oxford Univ. Press, 1954.
%D I. Sh. Slavutskii, A note on Bernoulli numbers, Jour. of Number Theory 53 (1995), 309-310.
%H Seiichi Manyama, <a href="/A069040/b069040.txt">Table of n, a(n) for n = 1..300</a>
%p A069040 := proc(n)
%p option remember;
%p if n=1 then
%p 1;
%p else
%p for k from procname(n-1)+1 do
%p if numer(bernoulli(2*k)) mod k = 0 then
%p return k;
%p end if;
%p end do:
%p end if;
%p end proc: # _R. J. Mathar_, Jan 06 2013
%t testb[n_] := Select[First/@FactorInteger[n], Mod[2n, #-1]==0&]=={}; Select[Range[200], testb]
%Y Cf. A070191, A070192, A070193.
%K nonn
%O 1,2
%A _Benoit Cloitre_, Apr 03 2002
%E More information from _Dean Hickerson_, Apr 26 2002
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