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Search: id:A125194
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| A125194 |
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Numerator of generalized harmonic number H((p-1)/2,2p)= Sum[ 1/k^(2p), {k,1,(p-1)/2}] divided by p^2 for prime p>3. |
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+0
1
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| 41, 1599366601, 10877829357646990581304675244472669289, 100935935338172297894217692920950359818733561, 92171760645951046128269964368997337060279474366101773350776936377920690568228839\ 34927465549747441
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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-1,2p) is divisible by p^2 for prime p>3 (see A120290(n)). The numerator of generalized harmonic number H((p-1)/2,2p) is divisible by p^2 for prime p>3.
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LINKS
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Eric Weisstein, Link to a section of The World of Mathematics: Harmonic number.
Eric Weisstein, Link to a section of The World of Mathematics: Wolstenholme's Theorem.
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FORMULA
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a(n) = Numerator[ Sum[ 1/k^(2*Prime[n]), {k,1,(Prime[n]-1)/2} ]] / Prime[n]^2 for n>2.
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EXAMPLE
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Prime[3] = 5.
a(3) = Numerator[ 1 + 1/2^10 ] / 5^2 = 1025 / 25 = 41.
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MATHEMATICA
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Do[p=Prime[k]; f=0; Do[f=f+1/n^(2p); g=Numerator[f]; If[IntegerQ[g/(p)^2], Print[{p, g/p^2}]], {n, 1, (p-1)/2}], {k, 1, 100}]
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CROSSREFS
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Cf. A120290, A119722, A001008, A007406, A007408, A007410.
Sequence in context: A112550 A114927 A087512 this_sequence A095189 A023932 A022074
Adjacent sequences: A125191 A125192 A125193 this_sequence A125195 A125196 A125197
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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), Jan 13 2007
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