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.

A357016 Decimal expansion of the asymptotic density of numbers whose exponents in their prime factorization are squares (A197680).

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%I A357016 #5 Sep 09 2022 04:19:00
%S A357016 6,4,1,1,1,5,1,6,1,3,5,9,3,5,1,4,3,1,4,4,7,7,0,6,1,8,3,8,4,4,2,4,4,6,
%T A357016 0,4,1,5,9,2,0,8,9,4,0,4,0,9,2,5,7,4,6,5,2,6,8,5,5,6,0,9,4,1,0,5,3,3,
%U A357016 0,7,2,3,9,3,8,3,2,0,4,0,9,7,3,4,5,4,2,1,1,8,4,6,7,4,0,0,6,9,3,5,6,3,6,3,5
%N A357016 Decimal expansion of the asymptotic density of numbers whose exponents in their prime factorization are squares (A197680).
%C A357016 Equivalently, the asymptotic density of numbers with an odd number of exponential divisors (A049419).
%H A357016 Vladimir Shevelev, <a href="http://arxiv.org/abs/1510.05914">Exponentially S-numbers</a>, arXiv:1510.05914 [math.NT], 2015-2016.
%F A357016 Equals Product_{p prime} (1 + Sum_{k>=2} (c(k)-c(k-1))/p^k), where c(k) is the characteristic function of the squares (A010052).
%e A357016 0.64111516135935143144770618384424460415920894040925...
%t A357016 $MaxExtraPrecision = m = 1000; em = 100; f[x_] := Log[1 + Sum[x^(e^2), {e, 2, em}] - Sum[x^(e^2 + 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, 105][[1]]
%Y A357016 Cf. A000290, A010052, A049419, A197680, A357017.
%K A357016 nonn,cons
%O A357016 0,1
%A A357016 _Amiram Eldar_, Sep 09 2022