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Search: id:A095820
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| A095820 |
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Numerators of some (trivial) upper bounds for Euler's Zeta-function Zeta(n). |
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2
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| 2, 11, 1465, 260467, 47541136609, 941124897061, 972240507397068973121, 7727206375538178489426059, 10338017533904483647451374351534201, 26038773922578490153470593775940352227
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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For the denominators see A095821.
Zeta(n):=sum(1/k^n,k=1..infty),n>=2, has (trivial) upper bound r(n):= a(n)/A095821(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)= numerator(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: A131316 A062636 A051254 this_sequence A101295 A131306 A145797
Adjacent sequences: A095817 A095818 A095819 this_sequence A095821 A095822 A095823
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KEYWORD
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nonn,easy,frac
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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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