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A120290
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Numerator of generalized harmonic number H(p-1,2p)= Sum[ 1/k^(2p), {k,1,p-1}] divided by p^2 for prime p>3.
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3
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OFFSET
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3,1
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COMMENTS
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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-1,2p) is divisible by p^2 for prime p>3.
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LINKS
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FORMULA
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a(n) = numerator[ Sum[ 1/k^(2*Prime[n]), {k,1,Prime[n]-1} ]] / Prime[n]^2 for n>2.
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EXAMPLE
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With prime(3) = 5, a(3) = numerator[ 1 + 1/2^10 + 1/3^10 + 1/4^10 ] / 5^2 = 61978938025 / 25 = 2479157521.
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MATHEMATICA
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Table[Numerator[Sum[1/k^(2*Prime[n]), {k, 1, Prime[n]-1}]], {n, 3, 7}]/Table[Prime[n]^2, {n, 3, 7}]
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CROSSREFS
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KEYWORD
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frac,nonn,bref
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AUTHOR
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STATUS
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approved
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