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Search: id:A119722
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| A119722 |
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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. |
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10
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| 2063, 2743174627, 19563315706517008974432827112201617, 2597378078067393746941400113704449589199274012223316613, 77747835861252969999146394856377841064474812149852606558597663885427788637948074\ 9840301120148933
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OFFSET
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3,1
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COMMENT
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Generalized harmonic number is H(n,m)= Sum[ 1/k^m, {k,1,n} ]. The numerator of generalized harmonic number H(p-1,p) is divisible by p^3 for prime p>3.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics: Wolstenholme's TheoremEric Weisstein's World of Mathematics, Link to a section of The World of Mathematics: Harmonic Number
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FORMULA
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a(n) = numerator[ Sum[ 1/k^Prime[n], {k,1,Prime[n]-1} ]] / Prime[n]^3 for n>2.
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EXAMPLE
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Prime[3] = 5.
a(3) = numerator[ 1 + 1/2^5 + 1/3^5 + 1/4^5 ] / 5^3 = 257875/125 = 2063.
Prime[4] = 7
a(4) = numerator[ 1 + 1/2^7 + 1/3^7 + 1/4^7 + 1/5^7 + 1/6^7 ] / 7^3 = 2743174627.
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MATHEMATICA
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Numerator[Table[Sum[1/k^Prime[n], {k, 1, Prime[n]-1}], {n, 3, 9}]]/Table[Prime[n]^3, {n, 3, 9}]
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CROSSREFS
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Cf. A099828, A099827, A001008, A007406, A007408, A007410.
Sequence in context: A045055 A069427 A106719 this_sequence A015993 A065217 A035871
Adjacent sequences: A119719 A119720 A119721 this_sequence A119723 A119724 A119725
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KEYWORD
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frac,nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 13 2006
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