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

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, 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, 0, 3, 0, 7, 0, 3, 2, 1, 1, 7, 2, 4, 6, 8, 3, 7, 7, 2, 3

Offset

1,4

Comments

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.

Links

Table of n, a(n) for n=1..87.

Maurice-Étienne Cloutier, Jean-Marie De Koninck, and Nicolas Doyon, On the powerful and squarefree parts of an integer, Journal of Integer Sequences, Vol. 17 (2014), Article 14.6.6.

Formula

Equals (4/3)*(zeta(3/2)/zeta(3)) * Product_{p prime} (1 - 1/p)*(1 + (1-1/p)/(p*(1 + 1/p^(3/2)))).

Example

1.115436631111013698931934302941096327033286649113053...

Mathematica

$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]]

Crossrefs

Cf. A057521, A055231, A328014.

Sequence in context: A183164 A364490 A019762 * A256099 A192918 A092156

Adjacent sequences: A328012 A328013 A328014 * A328016 A328017 A328018

Keyword

nonn,cons

Author

Amiram Eldar, Oct 01 2019

Status

approved