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%I #21 May 18 2020 11:32:51
%S 2,1,8,6,2,6,3,4,6,4,8,8,5,7,5,4,8,0,8,0,5,0,8,6,7,5,7,9,5,9,0,1,0,1,
%T 7,4,3,8,7,5,8,7,9,9,5,3,8,0,1,2,5,2,4,7,7,5,6,4,6,6,4,4,5,6,8,2,1,0,
%U 6,6,2,3,4,6,5,2,1,2,1,0,4,9,2,1,1,1,0,2,0,4,2,2,0,0,0,1,3,3
%N Decimal expansion of the normalized asymptotic mean of omega(m) when m is one of the values <= n taken by Euler's phi totient function.
%D Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.7. Euler Totient Constants, pp. 115-119.
%H G. C. Greubel, <a href="/A272983/b272983.txt">Table of n, a(n) for n = 1..10000</a>
%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, arXiv:2001.00578 [math.HO], 2020, p. 16.
%H Kevin Ford, <a href="http://www.math.uiuc.edu/~ford/wwwpapers/totients.pdf">The distribution of Totients</a>
%F 1/(1 - rho), where rho is A246746.
%e 2.186263464885754808050867579590101743875879953801252477564664456821...
%t digits = 98; F[x_?NumericQ] := NSum[((k+1)*Log[k+1] - k*Log[k] - 1)*x^k, {k, 1, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 1000]; rho = x /. FindRoot[F[x] == 1, {x, 1/2, 3/5}, WorkingPrecision -> digits + 10]; RealDigits[1/(1 - rho), 10, digits] // First
%Y Cf. A000010, A001221, A246746, A234614, A246751.
%K nonn,cons
%O 1,1
%A _Jean-François Alcover_, May 12 2016
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