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A130681
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Numerator of generalized harmonic number H(p-1,2p-1)= Sum[ 1/k^(2p-1), {k,1,p-1}] divided by p^3 for prime p>3.
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1
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41361119, 126941659254799099843, 201945187495172518712395211386399925751676163316330287629003467281801, 534565103485593943310791656810688803242468895931876288948761507813750601446840308490623197040810555162527973
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,1
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COMMENTS
| Generalized harmonic number is H(n,m)= Sum[ 1/k^m, {k,1,n} ]. The numerator of generalized harmonic number H(p-1,2p-1) is divisible by p^3 for prime p>3. Also the numerator of generalized harmonic number H(p-1,p) is divisible by p^3 for prime p>3. See A119722(n).
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LINKS
| Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 29 2007, Table of n, a(n) for n = 3..10
Eric Weisstein, Link to a section of The World of Mathematics: Wolstenholme's Theorem.
Eric Weisstein, Link to a section of The World of Mathematics: Harmonic Number.
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FORMULA
| a(n) = Numerator[ Sum[ 1/k^(2*Prime[n]-1), {k,1,Prime[n]-1} ] ] / Prime[n]^3 for n>2.
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EXAMPLE
| Prime[3] = 5.
a(3) = numerator[ 1 + 1/2^9 + 1/3^9 + 1/4^9 ] / 5^3 = 5170139875/125 = 41361119.
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MATHEMATICA
| Table[ Numerator[ Sum[ 1/k^(2*Prime[n]-1), {k, 1, Prime[n]-1} ] ] / Prime[n]^3, {n, 3, 10} ]
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CROSSREFS
| Cf. A119722 = Numerator of generalized harmonic number H(p-1, p)= Sum[ 1/k^p, {k, 1, p-1}] divided by p^3 for prime p>3.
Sequence in context: A017613 A015409 A178204 * A198168 A187963 A028520
Adjacent sequences: A130678 A130679 A130680 * A130682 A130683 A130684
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KEYWORD
| frac,nonn,uned
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 29 2007
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