cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A327839 Decimal expansion of the asymptotic density of numbers whose number of divisors is a power of 2 (A036537).

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%I A327839 #4 Sep 27 2019 19:45:36
%S A327839 6,8,7,8,2,7,1,3,9,4,4,3,6,2,4,8,8,1,0,6,3,5,1,0,8,2,4,5,4,9,8,7,0,9,
%T A327839 8,3,2,0,3,0,9,5,8,7,5,3,0,1,0,1,5,2,1,7,1,0,5,6,4,0,1,6,9,0,8,8,7,4,
%U A327839 8,4,9,1,6,4,6,2,8,2,9,6,3,5,9,4,7,0,7
%N A327839 Decimal expansion of the asymptotic density of numbers whose number of divisors is a power of 2 (A036537).
%H A327839 Vladimir Shevelev, <a href="http://doi.org/10.4064/aa8395-5-2016">S-exponential numbers</a>, Acta Arithmetica, Vol. 175, No. 4 (2016), pp. 385-395, <a href="https://www.math.bgu.ac.il/~shevelev/S_exp_numb.pdf">alternative link</a>.
%F A327839 Equals Product_{p prime} (1 - 1/p) * (1 + Sum_{i>=1} 1/p^(2^i-1)).
%F A327839 Equals lim_{k->oo} A036538(k)/2^k.
%e A327839 0.687827139443624881063510824549870983203095875301015...
%t A327839 $MaxExtraPrecision = 1000; m = 1000; em = 10; f[x_] := Log[(1 - x)*(1 + Sum[x^(2^e - 1), {e, 1, em}])]; c = Rest[CoefficientList[Series[f[x], {x, 0, m}], x] * Range[0, m]]; RealDigits[Exp[NSum[Indexed[c, k]*PrimeZetaP[k]/k, {k, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 100][[1]]
%Y A327839 Cf. A036537, A036538.
%K A327839 nonn,cons
%O A327839 0,1
%A A327839 _Amiram Eldar_, Sep 27 2019