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A247605 Decimal expansion of the coefficient c_md in c_md*log(N)^(1/rho), the asymptotic mean number of distinct factors in a random factorization of n <= N.

%I A247605 #24 Jun 11 2024 01:40:19
%S A247605 1,4,8,7,9,1,5,9,7,1,6,7,8,1,5,7,8,9,2,8,7,1,6,8,6,3,0,5,4,6,5,5,6,6,
%T A247605 0,7,2,7,9,1,9,8,8,4,9,0,4,5,2,7,1,7,9,1,8,9,7,1,1,1,7,9,7,4,5,3,8,5,
%U A247605 7,8,5,4,4,4,6,2,5,3,5,4,3,5,6,8,6,5,8,9,2,4,8,7,1,6,6,3,7,1,2,2,8
%N A247605 Decimal expansion of the coefficient c_md in c_md*log(N)^(1/rho), the asymptotic mean number of distinct factors in a random factorization of n <= N.
%D A247605 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.5. Kalmár’s Composition Constant, p. 293.
%H A247605 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, arXiv:2001.00578 [math.HO], 2020-2024, p. 37.
%F A247605 c_md = (-1/rho)*Gamma(-1/rho)*(-1/zeta'(rho))^(1/rho), where rho = 1.728647... is A107311, the real solution to zeta(rho) = 2.
%e A247605 1.48791597167815789287168630546556607279198849...
%t A247605 digits = 101; rho = x /. FindRoot[Zeta[x] == 2, {x, 2}, WorkingPrecision -> digits + 5]; cmd = (-1/rho)*Gamma[-1/rho]*(-1/Zeta'[rho])^(1/rho); RealDigits[cmd, 10, digits] // First
%Y A247605 Cf. A107311, A217598, A247667.
%K A247605 nonn,cons
%O A247605 1,2
%A A247605 _Jean-François Alcover_, Sep 22 2014