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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

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: 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.)