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A247668 Decimal expansion of the coefficient c_v in c_v*log(N), the asymptotic variance of the number of factors in a random factorization of n <= N.

%I A247668 #13 Feb 26 2025 05:54:16
%S A247668 3,0,8,4,0,3,4,4,4,6,0,8,0,7,7,0,0,1,6,3,3,6,0,7,7,2,6,1,7,4,5,8,7,9,
%T A247668 8,6,6,7,2,0,9,4,9,6,0,5,3,6,8,8,6,0,8,4,9,6,7,2,6,4,7,6,9,9,9,8,4,0,
%U A247668 0,0,9,3,6,0,2,2,0,0,9,2,3,6,6,4,9,5,3,8,3,2,1,5,8,1,3,5,1,9,0,0,6,7
%N A247668 Decimal expansion of the coefficient c_v in c_v*log(N), the asymptotic variance of the number of factors in a random factorization of n <= N.
%D A247668 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.5. Kalmár’s Composition Constant, p. 293.
%H A247668 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 37.
%F A247668 c_v = (-1/zeta'(rho))*(zeta''(rho)/zeta'(rho)^2 - 1), where rho = 1.728647... is A107311, the real solution to zeta(rho) = 2.
%e A247668 0.308403444608077001633607726174587986672094960536886...
%t A247668 digits = 102; rho = x /. FindRoot[Zeta[x] == 2, {x, 2}, WorkingPrecision -> digits+5]; cv = (-1/Zeta'[rho])*(Zeta''[rho]/Zeta'[rho]^2 - 1); RealDigits[cv, 10, digits] // First
%Y A247668 Cf. A107311, A217598, A247667.
%K A247668 nonn,cons
%O A247668 0,1
%A A247668 _Jean-François Alcover_, Sep 22 2014