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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
1, 5, 7, 71, 379, 2659 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..6.

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: 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

KEYWORD

hard,more,nonn

AUTHOR

Alexander Adamchuk, Mar 10 2007

STATUS

approved

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Last modified April 23 00:56 EDT 2021. Contains 343197 sequences. (Running on oeis4.)