A361062 Decimal expansion of the asymptotic mean of A073184(k)/A000005(k), the ratio between the number of cubefree divisors and the number of divisors.

9, 3, 9, 9, 7, 4, 3, 5, 2, 1, 7, 6, 4, 7, 7, 0, 7, 8, 4, 7, 0, 4, 4, 2, 5, 6, 2, 3, 8, 6, 0, 2, 5, 7, 2, 6, 7, 6, 9, 8, 4, 2, 3, 1, 0, 9, 7, 7, 9, 9, 6, 7, 3, 3, 0, 5, 9, 8, 1, 3, 8, 2, 1, 6, 7, 4, 6, 1, 3, 5, 9, 5, 5, 2, 0, 4, 4, 8, 0, 1, 3, 5, 9, 2, 5, 3, 1, 3, 0, 3, 8, 4, 8, 1, 0, 5, 1, 2, 9, 4, 6, 6, 6, 7, 1

Offset: 0

Author

Amiram Eldar, Mar 01 2023

Keywords

• nonn
• cons

Examples

			0.939974352176477078470442562386025726769842310977996...
		

Crossrefs

Cf. A000005, A073184, A361061 (mean of the inverse ratio).

Cf. A307869, A308043 (squarefree analog).

Programs

Mathematica

$MaxExtraPrecision = 1000; m = 1000; f[p_] := -(p-1)*(1+4*p+6*p^2*Log[1-1/p])/(2*p^2); c = Rest[CoefficientList[Series[Log[f[1/x]], {x, 0, m}], x]]; RealDigits[Exp[NSum[Indexed[c, n]*(PrimeZetaP[n]), {n, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 100][[1]]

Formula

Equals lim_{m->oo} (1/m) * Sum_{k=1..m} A073184(k)/A000005(k).

Equals Product_{p prime} (-(p-1)*(1+4*p+6*p^2*log(1-1/p))/(2*p^2)).