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

1,4

Links

Table of n, a(n) for n=1..105.

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)).

Example

1.109049677998737336345288587781671766009752629677303...

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]]

Prog

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

Crossrefs

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

Cf. A307869 (squarefree analog), A308043.

Sequence in context: A021529 A196398 A192932 * A301865 A370705 A309605

Adjacent sequences: A361058 A361059 A361060 * A361062 A361063 A361064

Keyword

nonn,cons

Author

Amiram Eldar, Mar 01 2023

Status

approved