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A112932 Denominator of rational values arising in an asymptotic formula for 1/(zeta(s)-1) as s-->infinity. 2

%I

%S 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,

%T 35,9,75,19,39,81,21,11,45,729,23,189,49,99,25,405,51,13,105,27,55,

%U 225,57,29,117,15,243,31,125,63,65,33,135

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

%H Andrei Vieru, <a href="http://arxiv.org/abs/1306.0496">Euler constant as a renormalized value of Riemann zeta function at its pole. Rationals related to Dirichlet L-functions</a>, arXiv:1306.0496 [math.GM], 2015.

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

%t 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 *)

%Y Cf. A112931, A112933.

%K frac,more,nonn

%O 0,2

%A _Benoit Cloitre_, Oct 06 2005

%E a(15)-a(33) computed by Andrei Vieru, added by _Vaclav Kotesovec_, Aug 11 2019

%E Terms a(34) and beyond from _Vaclav Kotesovec_, Aug 11 2019

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Last modified April 13 01:36 EDT 2021. Contains 342934 sequences. (Running on oeis4.)