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A128465
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Numbers n such that n divides the numerator of alternating Harmonic number H'((n+1)/2) = A058313((n+1)/2).
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1
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..6.
Eric Weisstein's World of Mathematics, Harmonic Number
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MATHEMATICA
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f=0; Do[ f = f + (-1)^(n+1)*1/n; g = Numerator[f]; If[ IntegerQ[ g/(2n-1) ], Print[2n-1]], {n, 1, 3000} ]
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CROSSREFS
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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.
Sequence in context: A308397 A308848 A109715 * A098967 A107140 A141746
Adjacent sequences: A128462 A128463 A128464 * A128466 A128467 A128468
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KEYWORD
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hard,more,nonn
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AUTHOR
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Alexander Adamchuk, Mar 10 2007
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STATUS
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approved
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