%I #9 Apr 14 2020 03:27:49
%S 7,1,5,5,5,4,4,2,2,2,5,4,9,2,1,8,6,6,7,9,8,1,1,2,4,3,8,1,9,0,9,7,9,1,
%T 9,3,3,1,9,8,6,2,4,7,1,0,2,2,1,9,7,4,9,1,8,2,5,4,9,1,2,6,8,5,6,7,7,4,
%U 8,4,8,9,4,3,6,6,4,7,0,6,1,0,8,5,5,9,8
%N Decimal expansion of Sum_{k >= 1} 2^(-sigma(k)), where sigma is the sum of divisors function (A000203).
%C This constant is irrational (Erdős and Graham, 1980).
%H Paul Erdős and Ronald L. Graham, <a href="http://www.math.ucsd.edu/~fan/ron/papers/80_11_number_theory.pdf">Old and new problems and results in combinatorial number theory</a>, L'enseignement Mathématique, Université de Genève, 1980.
%e 0.71555442225492186679811243819097919331986247102219...
%t RealDigits[Sum[2^(-DivisorSigma[1, n]), {n, 1, 2000}], 10, 100][[1]]
%o (PARI) suminf(k=1, 1/2^sigma(k)) \\ _Michel Marcus_, Apr 14 2020
%Y Cf. A000203, A334071.
%K nonn,cons
%O 0,1
%A _Amiram Eldar_, Apr 13 2020
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