cp's OEIS Frontend

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

%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