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%I #16 Feb 19 2022 06:05:31
%S 1,2,4,2,0,6,2,0,9,4,8,1,2,4,1,4,9,4,5,7,9,7,8,4,5,4,8,1,8,9,4,6,2,9,
%T 6,6,8,9,7,3,4,0,3,9,7,8,2,5,0,4,2,5,8,8,4,6,2,7,1,3,8,1,6,7,2,5,3,3,
%U 9,1,1,8,4,4,7,0,6,2,8,8,4,6,5,8,2,4,1
%N Decimal expansion of Sum_{k>=1} sigma(k)/(k*2^k) where sigma(k) is the sum of divisors of k (A000203).
%H Maxie Dion Schmidt, <a href="https://arxiv.org/abs/2004.02976">A catalog of interesting and useful Lambert series identities</a>, arXiv:2004.02976 [math.NT], 2020.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertSeries.html">Lambert Series</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lambert_series">Lambert series</a>.
%F Equals Sum_{k>=1} (A017665(k)/A017666(k))/2^k.
%F Equals Sum_{k>=1} 1/(k*(2^k - 1)) = Sum_{k>=1} 1/A066524(k).
%F Equals -Sum_{k>=1} log(1-2^(-k)).
%F Equals -log(A048651). - _Amiram Eldar_, Feb 19 2022
%e 1.242062094812414945797845481894629668973403978250425...
%t RealDigits[Sum[1/n/(2^n - 1), {n, 1, 500}], 10, 100][[1]]
%t RealDigits[-Log[QPochhammer[1/2]], 10, 120][[1]] (* _Vaclav Kotesovec_, Feb 18 2021 *)
%o (PARI) suminf(x = 1, sigma(x)/(x*2^x)) \\ _David A. Corneth_, Jun 21 2020
%Y Cf. A000203, A017665, A017666, A048651, A065442, A066524, A066766, A256936, A335763.
%K nonn,cons
%O 1,2
%A _Amiram Eldar_, Jun 21 2020
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