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 A128465 Numbers k such that k divides the numerator of alternating Harmonic number H'((k+1)/2) = A058313((k+1)/2). 1
 1, 5, 7, 71, 379, 2659 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For k > 1 all 5 listed terms are primes. Numbers k such that k divides the numerator of alternating Harmonic number H'((k-1)/2) = A058313((k-1)/2) are listed in A128464 = {1073, 3511, ...}. Both known terms of A128464 are the Wieferich primes A001220 = {1093, 3511, ...}. Primes p such that p^2 divides 2^(p-1) - 1. LINKS Eric Weisstein's World of Mathematics, Harmonic Number MATHEMATICA f=0; Do[ f = f + (-1)^(n+1)*1/n; g = Numerator[f]; If[ IntegerQ[ g/(2n-1) ], Print[2n-1]], {n, 1, 3000} ] CROSSREFS Cf. A001008 (Wolstenholme numbers: numbers k such that the numerator of harmonic number H(k) = Sum_{i=1..k} 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. Sequence in context: A308397 A308848 A109715 * A098967 A107140 A141746 Adjacent sequences:  A128462 A128463 A128464 * A128466 A128467 A128468 KEYWORD hard,more,nonn,changed AUTHOR Alexander Adamchuk, Mar 10 2007 STATUS approved

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Last modified June 22 12:56 EDT 2021. Contains 345380 sequences. (Running on oeis4.)