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A128465 Numbers n such that n divides the numerator of alternating Harmonic number H'((n+1)/2) = A058313((n+1)/2). 1

%I

%S 1,5,7,71,379,2659

%N Numbers n such that n divides the numerator of alternating Harmonic number H'((n+1)/2) = A058313((n+1)/2).

%C For n>1 all 5 listed terms are primes. Numbers n such that n divides the numerator of alternating Harmonic number H'((n-1)/2) = A058313((n-1)/2) are listed in A128464(n) = {1073, 3511, ...}. Both known terms of A128464(n) are the Wieferich primes A001220(n) = {1093, 3511, ...} Primes p such that p^2 divides 2^(p-1) - 1.

%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 = Wolstenholme numbers: numerator of harmonic number H(n)=Sum_{i=1..n} 1/i. Cf. A058313 = Numerator of the n-th alternating harmonic number H'(n). Cf. A001220 = Wieferich primes p: p^2 divides 2^(p-1) - 1. Cf. A128463, A128464, A125854, A121999.

%K hard,more,nonn

%O 1,2

%A _Alexander Adamchuk_, Mar 10 2007

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Last modified May 7 20:36 EDT 2021. Contains 343652 sequences. (Running on oeis4.)