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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

For the denominators see A095821.

Zeta(n):=sum(1/k^n,k=1..infty),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(1/k^n, k=1..n-1) + 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: A131316 A062636 A051254 * A101295 A131306 A145797

Adjacent sequences:  A095817 A095818 A095819 * A095821 A095822 A095823

KEYWORD

nonn,easy,frac

AUTHOR

Wolfdieter Lang, Jun 11 2004

STATUS

approved

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Last modified June 24 22:01 EDT 2019. Contains 324337 sequences. (Running on oeis4.)