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Search: id:A095821
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| A095821 |
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Denominators of some (trivial) upper bounds for Euler's Zeta-function Zeta(n). |
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2
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| 1, 8, 1296, 248832, 46656000000, 933120000000, 968265199641600000000, 7711694390034432000000000, 10327742657402407212810240000000000, 26025911496654066176281804800000000000
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OFFSET
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2,2
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COMMENT
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For the numerators see A095820.
Zeta(n):=sum(1/k^n,k=1..infty),n>=2, has (trivial) upper bound r(n):= A095820(n)/a(n). See the W. Lang link.
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LINKS
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W. Lang, r(n) numbers and comments with a proof.
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FORMULA
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a(n)= denominators(r(n)), with rational r(n):= sum(1/k^n, k=1..n-1) + 1/((n-1)*(n-1)!), n>=2, written in lowest terms. For n*n! see A001563(n).
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EXAMPLE
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The positive rationals r(n), n>=2: 2/1, 11/8, 1465/1296, 260467/248832, 47541136609/46656000000, ...
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CROSSREFS
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Sequence in context: A160008 A027668 A162139 this_sequence A091868 A162090 A017187
Adjacent sequences: A095818 A095819 A095820 this_sequence A095822 A095823 A095824
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Jun 11 2004
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