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.

A328015 Decimal expansion of the growth constant for the number of terms of A328014 (numbers whose powerful part is larger than their powerfree part).

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%I A328015 #8 Feb 18 2023 10:55:37
%S A328015 1,1,1,5,4,3,6,6,3,1,1,1,1,0,1,3,6,9,8,9,3,1,9,3,4,3,0,2,9,4,1,0,9,6,
%T A328015 3,2,7,0,3,3,2,8,6,6,4,9,1,1,3,0,5,3,1,6,1,6,7,1,1,4,7,6,3,9,5,7,6,8,
%U A328015 0,3,0,7,0,3,2,1,1,7,2,4,6,8,3,7,7,2,3
%N A328015 Decimal expansion of the growth constant for the number of terms of A328014 (numbers whose powerful part is larger than their powerfree part).
%C A328015 Cloutier et al. showed that the number of terms of A328014 below x is D0 * x^(3/4) + O(x^(2/3)*log(x)), where D0 is this constant.
%H A328015 Maurice-Étienne Cloutier, Jean-Marie De Koninck, and Nicolas Doyon, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Cloutier/cloutier2.html">On the powerful and squarefree parts of an integer</a>, Journal of Integer Sequences, Vol. 17 (2014), Article 14.6.6.
%F A328015 Equals (4/3)*(zeta(3/2)/zeta(3)) * Product_{p prime} (1 - 1/p)*(1 + (1-1/p)/(p*(1 + 1/p^(3/2)))).
%e A328015 1.115436631111013698931934302941096327033286649113053...
%t A328015 $MaxExtraPrecision = 500; m = 500; f[x_] := (1 - x)*(1 + (1 - x)*x/(1 + x^(3/2))); c = LinearRecurrence[{2, -3, 2, 1, -3, 3, -1}, {0, 0, 0, -8, -5, 6, 14}, m]; RealDigits[(4/3)*(Zeta[3/2]/Zeta[3])*f[1/2]*f[1/3]*Exp[NSum[Indexed[c, n]*(PrimeZetaP[n/2] - 1/2^(n/2) - 1/3^(n/2))/n, {n, 3, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 100][[1]]
%Y A328015 Cf. A057521, A055231, A328014.
%K A328015 nonn,cons
%O A328015 1,4
%A A328015 _Amiram Eldar_, Oct 01 2019