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A095821
Denominators of some (trivial) upper bounds for Euler's Zeta-function Zeta(n).
1
1, 8, 1296, 248832, 46656000000, 933120000000, 968265199641600000000, 7711694390034432000000000, 10327742657402407212810240000000000, 26025911496654066176281804800000000000
OFFSET
2,2
COMMENTS
For the numerators see A095820.
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.
FORMULA
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).
EXAMPLE
The positive rationals r(n), n >= 2: 2/1, 11/8, 1465/1296, 260467/248832, 47541136609/46656000000, ...
CROSSREFS
Sequence in context: A160008 A251699 A162139 * A340562 A176113 A091868
KEYWORD
nonn,frac,easy
AUTHOR
Wolfdieter Lang, Jun 11 2004
STATUS
approved