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Search: id:A103345
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| A103345 |
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Numerators of sum(1/k^6,k=1..n)=:Zeta(6,n). |
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19
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| 1, 65, 47449, 3037465, 47463376609, 47464376609, 5584183099672241, 357389058474664049, 260537105518334091721, 52107472322919827957, 92311616995117182948130877, 92311647383100199924330877
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For the denominators see A103346. For the rationals Zeta(k,n) for k=1..10, n=1..20, see the W. Lang link.
a(n) gives the partial sums, Zeta(6,n) of Euler's (later Riemann's) Zeta(6). Zeta(k,n), k>=2, is sometimes also called H(k,n) because for k=1 these would be the harmonic numbers A001008/A002805. However, H(1,n) does not give partial sums of a convergent series.
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LINKS
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W. Lang, Rational Zeta(k,n).
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FORMULA
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a(n)=numerator(sum(1/k^6, k=1..n)).
G.f. for rationals Zeta(6, n): polylogarithm(6, x)/(1-x).
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MATHEMATICA
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s=0; lst={}; Do[s+=n^1/n^7; AppendTo[lst, Numerator[s]], {n, 3*4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 24 2009]
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CROSSREFS
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For k=1..5 see: A001008/A002805, A007406/A007407, A007408/A007409, A007410/A007480, A099828/A069052.
Sequence in context: A093265 A120801 A084225 this_sequence A061688 A015072 A015039
Adjacent sequences: A103342 A103343 A103344 this_sequence A103346 A103347 A103348
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Feb 15 2005
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