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%I #5 Nov 14 2023 09:16:20
%S 3,6,0,4,4,4,7,3,4,1,9,7,1,9,4,6,7,4,4,8,9,3,6,4,8,4,7,3,6,2,3,5,8,8,
%T 3,5,6,0,0,4,9,5,4,8,7,0,6,4,9,9,8,7,5,0,1,3,8,3,6,2,6,3,1,5,0,9,6,6,
%U 2,9,5,0,1,7,0,7,1,3,4,9,6,6,9,1,7,8,2,2,8,9,9,1,6,9,9,2,7,5,4,4,2,7,0,3,8
%N Decimal expansion of Sum_{k>=1} sigma(k)/(2^k-1), 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. See eq. (6.1c), p. 13.
%H Michael I. Shamos, <a href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.366.9997">Shamos's catalog of the real numbers</a>, 2011. See p. 526.
%F Equals Sum_{k>=1} d(k)/((2^k-1)*(1-1/2^k)), where d(k) is the number of divisors of k (A000005).
%e 3.60444734197194674489364847362358835600495487064998...
%p with(numtheory): evalf(sum(sigma(k)/(2^k-1), k = 1..infinity), 120)
%t RealDigits[Sum[DivisorSigma[1,n]/(2^n-1), {n, 1, 500}], 10, 120][[1]]
%o (PARI) suminf(k = 1, sigma(k)/(2^k-1))
%o (PARI) suminf(k = 1, numdiv(k)/((2^k-1)*(1-1/2^k)))
%Y Cf. A000005, A000203.
%Y Similar constants: A065442, A066766, A116217, A335763, A335764.
%K nonn,cons
%O 1,1
%A _Amiram Eldar_, Nov 14 2023
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