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%I #28 Jan 30 2022 15:58:17
%S 2,3,4,1,4,9,1,3,0,1,3,4,8,0,9,2,0,6,4,8,5,1,1,1,6,7,2,8,1,3,8,7,2,9,
%T 1,8,5,4,6,3,6,1,0,3,4,7,8,6,5,1,3,8,9,8,5,2,2,4,2,1,3,8,6,7,1,0,2,3,
%U 8,1,9,8,6,6,2,8,7,9,2,3,2,2,5,6,7,8,8,7,9,5,0,1,8,7,8,3,9,1,2,6,6,5,5,3,4
%N Decimal expansion of the Sum_{k>=1} 1/(6^k - 1).
%H G. C. Greubel, <a href="/A248723/b248723.txt">Table of n, a(n) for n = 0..10000</a>
%F Equals Sum_{k>=1} d(k)/6^k, where d(k) is the number of divisors of k (A000005). - _Amiram Eldar_, Jun 22 2020
%e 0.2341491301348092064851116728138729185463610347865138985224213867102381986628...
%p evalf(sum(1/(6^k-1), k=1..infinity),120); # _Vaclav Kotesovec_, Oct 18 2014
%p # second program with faster converging series
%p evalf( add( (1/6)^(n^2)*(1 + 2/(6^n - 1)), n = 1..11), 105); # _Peter Bala_, Jan 30 2022
%t x = 1/6; RealDigits[ Sum[ DivisorSigma[0, k] x^k, {k, 1000}], 10, 105][[1]] (* after an observation and the formula of _Amarnath Murthy_, see A073668 *)
%o (PARI) suminf(k=1, 1/(6^k-1)) \\ _Michel Marcus_, Oct 18 2014
%Y Cf. A000005, A065442, A073668, A214369, A248721, A248722, A248724, A248725, A248726.
%K nonn,cons
%O 0,1
%A _Robert G. Wilson v_, Oct 12 2014
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