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%I #9 Apr 14 2020 03:27:41
%S 2,0,8,5,5,6,1,8,8,2,5,9,7,4,1,4,6,5,2,6,3,0,3,8,7,0,8,3,2,8,4,7,4,7,
%T 5,6,1,6,1,2,1,0,7,7,6,0,3,2,3,8,7,3,7,1,9,4,7,5,7,9,3,8,8,3,1,3,6,1,
%U 8,0,1,3,3,7,1,0,5,8,8,2,1,7,1,0,3,1,9
%N Decimal expansion of Sum_{k >= 1} 2^(-phi(k)), where phi is the Euler totient function (A000010).
%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 2.08556188259741465263038708328474756161210776032387...
%t RealDigits[Sum[2^(-EulerPhi[n]), {n, 1, 2000}], 10, 100][[1]]
%o (PARI) suminf(k=1, 1/2^eulerphi(k)) \\ _Michel Marcus_, Apr 14 2020
%Y Cf. A000010, A334072.
%K nonn,cons
%O 1,1
%A _Amiram Eldar_, Apr 13 2020
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