A095821 Denominators of some (trivial) upper bounds for Euler's Zeta-function Zeta(n).

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.

Links

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

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

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

Cf. A001563, A095820.

Sequence in context: A160008 A251699 A162139 * A340562 A176113 A091868

Adjacent sequences: A095818 A095819 A095820 * A095822 A095823 A095824

Keyword

nonn,frac,easy

Author

Wolfdieter Lang, Jun 11 2004

Status

approved