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%I #21 Jan 17 2020 16:17:04
%S 5,5,0,0,1,0,0,0,5,4,1,3,1,5,4,4,9,1,8,3,3,0,5,8,1,2,6,7,0,2,2,2,2,1,
%T 9,6,4,6,1,1,6,8,2,2,7,1,0,2,7,1,4,0,4,0,9,8,8,8,3,9,6,5,8,5,8,9,2,9,
%U 0,5,3,0,6,6,6,6,0,5,6,4,8,5,9,5,1,1,8,7,2,0,6,5,2,3,5,3,4,6,6,5,4
%N Decimal expansion of the coefficient c_m in c_m*log(N), the asymptotic mean number of factors in a random factorization of n <= N.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.5. Kalmár’s Composition Constant, p. 293.
%H Steven R. Finch, <a href="https://web.archive.org/web/20160511034134/http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 41.
%F c_m = -1/zeta'(rho), where rho = 1.728647... is A107311, the real solution to zeta(rho) = 2.
%F Residue_{s = rho} 1/(2 - Zeta(s)). - _Vaclav Kotesovec_, Nov 04 2018
%e 0.55001000541315449183305812670222219646116822710271404...
%t digits = 101; rho = x /. FindRoot[Zeta[x] == 2, {x, 2}, WorkingPrecision -> digits+5]; cm = -1/Zeta'[rho]; RealDigits[cm, 10, digits] // First
%Y Cf. A107311, A129373, A129374, A129375, A217598, A247668.
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, Sep 22 2014
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