A361061 Decimal expansion of the asymptotic mean of A000005(k)/A073184(k), the ratio between the number of divisors and the number of cubefree divisors.

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

Offset: 1

Author

Amiram Eldar, Mar 01 2023

Keywords

• nonn
• cons

Examples

			1.109049677998737336345288587781671766009752629677303...
		

Crossrefs

Cf. A000005, A073184, A361062 (mean of the inverse ratio).

Cf. A307869 (squarefree analog), A308043.

Programs

Mathematica

$MaxExtraPrecision = 1000; m = 1000; f[p_] := 1 + 1/(3*(p - 1)*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]]

PARI

prodeulerrat(1 + 1/(3*(p-1)*p^2))

Formula

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

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