

A112932


Denominator of rational values arising in an asymptotic formula for 1/(zeta(s)1) as s>infinity.


2



1, 3, 1, 9, 5, 3, 27, 7, 15, 9, 5, 81, 21, 11, 45, 25, 13, 27, 7, 15, 243, 63, 33, 135, 17, 35, 9, 75, 19, 39, 81, 21, 11, 45, 729, 23, 189, 49, 99, 25, 405, 51, 13, 105, 27, 55, 225, 57, 29, 117, 15, 243, 31, 125, 63, 65, 33, 135
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..57.
Andrei Vieru, Euler constant as a renormalized value of Riemann zeta function at its pole. Rationals related to Dirichlet Lfunctions, arXiv:1306.0496 [math.GM], 2015.


EXAMPLE

1/(zeta(s)1)=2^s(4/3)^s1+(8/9)^s(4/5)^s+(2/3)^s(16/27)^s(4/7)^s+2*(8/15)^s2*(4/9)^s+(2/5)^s+(32/81)^s+2*(8/21)^s(4/11)^s3*(16/45)^s+o((16/45)^x) and here sequence consists of denominators of 2/1,4/3,1/1,8/9,4/5,...


MATHEMATICA

nmax = 20; lz = ConstantArray[0, nmax]; ax = 0; Do[le = Exp[Limit[Log[Abs[(1/(Zeta[x]  1)  ax)]]/x, x > Infinity]]; ls = Limit[(1/(Zeta[x]  1)  ax)/le^x, x > Infinity]; ax = ax + ls*le^x; lz[[j]] = le; , {j, 1, nmax}]; Denominator[lz] (* Vaclav Kotesovec, Aug 11 2019 *)


CROSSREFS

Cf. A112931, A112933.
Sequence in context: A050155 A270236 A140714 * A337680 A077895 A105539
Adjacent sequences: A112929 A112930 A112931 * A112933 A112934 A112935


KEYWORD

frac,more,nonn


AUTHOR

Benoit Cloitre, Oct 06 2005


EXTENSIONS

a(15)a(33) computed by Andrei Vieru, added by Vaclav Kotesovec, Aug 11 2019
Terms a(34) and beyond from Vaclav Kotesovec, Aug 11 2019


STATUS

approved



