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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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1
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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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COMMENTS
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Zeta(n) := Sum_{k>=1} 1/k^n, 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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FORMULA
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a(n) = denominator(r(n)), with rational r(n) := Sum_{k=1..n-1} 1/k^n + 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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KEYWORD
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nonn,frac,easy
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AUTHOR
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STATUS
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approved
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