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%I #12 Jan 22 2021 09:00:28
%S 7,0,9,9,2,8,5,1,7,8,8,9,0,9,0,7,1,1,4,0,3,3,1,2,5,0,2,2,1,6,4,7,5,3,
%T 6,6,3,1,5,7,6,0,8,8,3,3,2,1,1,8,9,5,9,7,8,8,3,9,2,3,7,7,4,2,8,8,9,1,
%U 2,8,8,9,1,1,2,2,6,4,5,8,7,1,7,3,5,5,4
%N Decimal expansion of Sum_{k>=1} sigma_2(k)/2^k where sigma_2(k) is the sum of squares of divisors of k (A001157).
%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} k^2/(2^k - 1).
%F Faster converging series: Sum_{n >= 1} (1/2)^(n^2)*( n^2*(8^n) - ((n-1)^2 - 2)*4^n - ((n+1)^2 - 2)*(2^n) + n^2 )/(2^n - 1)^3. - _Peter Bala_, Jan 19 2021
%e 7.099285178890907114033125022164753663157608833211895...
%p evalf(add( (1/2)^(n^2)*( n^2*(8^n) - ((n-1)^2 - 2)*4^n - ((n+1)^2 - 2)*(2^n) + n^2 )/(2^n - 1)^3, n = 1..20 ), 100); # _Peter Bala_, Jan 22 2021
%t RealDigits[Sum[n^2/(2^n - 1), {n, 1, 500}], 10, 100][[1]]
%Y Cf. A001157, A065442, A066766, A227989, A256936, A335764.
%K nonn,cons
%O 1,1
%A _Amiram Eldar_, Jun 21 2020
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