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%I #15 Nov 30 2022 11:09:09
%S 1,5,7,71,379,2659
%N Numbers k such that k divides the numerator of alternating Harmonic number H'((k+1)/2) = A058313((k+1)/2).
%C For k > 1 all 5 listed terms are primes.
%C The only known numbers k such that k divides the numerator of alternating Harmonic number H'((k-1)/2) = A058313((k-1)/2) are the Wieferich primes (A001220): 1093 and 3511.
%C An odd prime p = prime(n) belongs to this sequence iff Fermat quotient A007663(n) == A130912(n) == 2*(-1)^((p+1)/2) (mod p). - _Max Alekseyev_, Nov 30 2022
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>
%t f=0; Do[ f = f + (-1)^(n+1)*1/n; g = Numerator[f]; If[ IntegerQ[ g/(2n-1) ], Print[2n-1]], {n,1,3000} ]
%Y Cf. A001008, A007663, A001220, A058313, A125854, A121999, A130912.
%K hard,more,nonn
%O 1,2
%A _Alexander Adamchuk_, Mar 10 2007
%E Edited by _Max Alekseyev_, Nov 30 2022
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