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%I #7 Jun 13 2021 13:12:20
%S 3,5,6,9,0,4,9,6,5,2,4,9,9,5,7,0,7,6,1,2,2,0,0,5,3,0,2,0,1,3,9,9,6,4,
%T 5,9,1,3,6,0,6,6,6,8,2,6,2,5,7,3,8,4,4,2,9,6,8,7,8,8,0,2,0,1,2,7,7,4,
%U 3,4,4,2,1,4,1,8,7,2,1,3,8,5,5,3,2,1,5
%N Decimal expansion of lim_{m->oo} (sqrt(log(m))/m^2) Sum_{k=1..m} sigma(k)/d(k), where d(k) is the number of divisors of k (A000005) and sigma(k) is their sum (A000203).
%H Paul T. Bateman, Paul Erdös, Carl Pomerance, and E. G. Straus, <a href="https://doi.org/10.1007/BFb0096462">The arithmetic mean of the divisors of an integer</a>, in: Marvin I. Knopp (ed.), Analytic Number Theory, Proceedings of a Conference Held at Temple University, Philadelphia, May 12-15, 1980, Lecture Notes in Mathematics, Vol 899, Springer, Berlin, Heidelberg, 1981, pp. 197-220, <a href="https://www.renyi.hu/~p_erdos/1981-37.pdf">alternative link</a>.
%H Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 162.
%F Equals (1/(2*sqrt(Pi))) * Product_{p prime} p^(3/2) * log(1 + 1/p) / sqrt(p-1).
%e 0.35690496524995707612200530201399645913606668262573...
%t $MaxExtraPrecision = 1000; m = 1000; f[x_] := Log[1 + x]/x/Sqrt[1 - x]; c = Rest[CoefficientList[Series[Log[f[x]], {x, 0, m}], x]]; RealDigits[(1/2/ Sqrt[Pi])*Exp[NSum[Indexed[c, k]*PrimeZetaP[k], {k, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 100][[1]]
%Y Cf. A000005, A000203, A057020, A057021.
%K nonn,cons
%O 0,1
%A _Amiram Eldar_, May 10 2019
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