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A130681 Sum[ 1/k^(2p-1), {k,1,p-1}] divided by p^3, for prime p>3. 2
41361119, 126941659254799099843, 201945187495172518712395211386399925751676163316330287629003467281801, 534565103485593943310791656810688803242468895931876288948761507813750601446840308490623197040810555162527973 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,1
COMMENTS
The generalized harmonic number is H(n,m) = Sum[ 1/k^m, {k,1,n} ]. The numerator of H(p-1,2p-1) is divisible by p^3 for prime p>3. Also the numerator of H(p-1,p) is divisible by p^3 for prime p>3. See A119722(n).
LINKS
Alexander Adamchuk, Table of n, a(n) for n = 3..10
Eric Weisstein's World of Mathematics, Wolstenholme's Theorem
Eric Weisstein's World of Mathematics, Harmonic Number
FORMULA
a(n) = Numerator[ Sum[ 1/k^(2*Prime[n]-1), {k,1,Prime[n]-1} ] ] / Prime[n]^3 for n>2.
a(n) = A228426(A000040(n))/A000040(n)^3.
EXAMPLE
Prime[3] = 5.
a(3) = numerator[ 1 + 1/2^9 + 1/3^9 + 1/4^9 ] / 5^3 = 5170139875/125 = 41361119.
MATHEMATICA
Table[ Numerator[ Sum[ 1/k^(2*Prime[n]-1), {k, 1, Prime[n]-1} ] ] / Prime[n]^3, {n, 3, 10} ]
PROG
(PARI) a(n)=p=prime(n); numerator(sum(i=1, p-1, 1/i^(2*p-1)))/p^3 \\ Ralf Stephan, Nov 10 2013
CROSSREFS
Cf. A119722.
Sequence in context: A015409 A178204 A334583 * A261658 A274812 A251306
KEYWORD
frac,nonn
AUTHOR
Alexander Adamchuk, Jun 29 2007
EXTENSIONS
Edited by Ralf Stephan, Nov 10 2013
STATUS
approved

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Last modified June 23 22:09 EDT 2024. Contains 373661 sequences. (Running on oeis4.)