A095820 Numerators of some (trivial) upper bounds for Euler's Zeta-function Zeta(n).

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.

Links

Table of n, a(n) for n=2..11.

W. Lang, r(n) numbers and comments with a proof.

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

Adjacent sequences: A095817 A095818 A095819 * A095821 A095822 A095823

Keyword

nonn,easy,frac

Author

Wolfdieter Lang, Jun 11 2004

Status

approved