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%I #9 Jul 16 2021 02:38:18
%S 1,0,6,8,3,8,9,9,3,0,0,7,8,4,1,2,3,2,0,0,2,0,8,4,7,6,5,9,0,1,7,5,8,2,
%T 3,8,2,2,4,7,2,8,9,6,0,8,6,5,5,2,8,0,7,2,1,4,9,7,8,0,7,0,7,6,0,3,1,5,
%U 3,1,6,7,9,1,8,6,4,7,6,0,7,0,5,7,4,4,1,9,7,3,0,9,2,6,3,9,3,7,8,6
%N Decimal expansion of Sum_{k>=1} A089723(k)/2^k.
%C This constant is irrational (Golomb, 1973).
%H Solomon W. Golomb, <a href="http://dx.doi.org/10.1016/0022-314X(73)90047-4">A new arithmetic function of combinatorial significance</a>, Journal of Number Theory, Vol. 5, No. 3 (1973), pp. 218-223.
%e 1.06838993007841232002084765901758238224728960865528...
%t f[n_] := DivisorSigma[0, GCD @@ FactorInteger[n][[;; , 2]]]; RealDigits[Sum[f[n]/2^n, {n, 1, 1000}], 10, 100][[1]]
%o (PARI) 1/2 + suminf(k=2, numdiv(gcd(factor(k)[, 2]))/2^k) \\ _Michel Marcus_, Jul 16 2021
%Y Cf. A089723.
%K nonn,cons
%O 1,3
%A _Amiram Eldar_, Jul 15 2021