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A095820
Numerators of some (trivial) upper bounds for Euler's Zeta-function Zeta(n).
2
2, 11, 1465, 260467, 47541136609, 941124897061, 972240507397068973121, 7727206375538178489426059, 10338017533904483647451374351534201, 26038773922578490153470593775940352227
OFFSET
2,1
COMMENTS
For the denominators see A095821.
Zeta(n) := Sum_{k>=1} 1/k^n, n >= 2, has (trivial) upper bound r(n):= a(n)/A095821(n). See the W. Lang link.
FORMULA
a(n) = numerator(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: A343900 A343929 A051254 * A101295 A131306 A145797
KEYWORD
nonn,easy,frac
AUTHOR
Wolfdieter Lang, Jun 11 2004
STATUS
approved