cp's OEIS Frontend

A335763 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).

%I A335763 #12 Jan 22 2021 09:00:28
%S A335763 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 A335763 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 A335763 2,8,8,9,1,1,2,2,6,4,5,8,7,1,7,3,5,5,4
%N A335763 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 A335763 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 A335763 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertSeries.html">Lambert Series</a>.
%H A335763 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lambert_series">Lambert series</a>.
%F A335763 Equals Sum_{k>=1} k^2/(2^k - 1).
%F A335763 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 A335763 7.099285178890907114033125022164753663157608833211895...
%p A335763 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 A335763 RealDigits[Sum[n^2/(2^n - 1), {n, 1, 500}], 10, 100][[1]]
%Y A335763 Cf. A001157, A065442, A066766, A227989, A256936, A335764.
%K A335763 nonn,cons
%O A335763 1,1
%A A335763 _Amiram Eldar_, Jun 21 2020