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

0,1

Links

Table of n, a(n) for n=0..104.

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)).

Example

0.939974352176477078470442562386025726769842310977996...

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]]

Crossrefs

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

Cf. A307869, A308043 (squarefree analog).

Sequence in context: A196829 A019879 A334376 * A003565 A238105 A363872

Adjacent sequences: A361059 A361060 A361061 * A361063 A361064 A361065

Keyword

nonn,cons

Author

Amiram Eldar, Mar 01 2023

Status

approved