A361060 Decimal expansion of the asymptotic mean of A286324(k)/A000005(k), the ratio between the number of bi-unitary divisors and the number of divisors.

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

Offset

0,1

Links

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

Eric Weisstein's World of Mathematics, Biunitary Divisor.

Formula

Equals lim_{m->oo} (1/m) * Sum_{k=1..m} A286324(k)/A000005(k).

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

Example

0.901241806826482255139197485094387558982811533821787...

Mathematica

$MaxExtraPrecision = 1000; m = 1000; f[p_] := 2 - 1/p - (p - 1)*Log[(p + 1)/(p - 1)]/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, A286324, A361059 (mean of the inverse ratio).

Cf. A307869, A308043 (unitary analog).

Sequence in context: A158336 A021530 A110909 * A364830 A345738 A197070

Adjacent sequences: A361057 A361058 A361059 * A361061 A361062 A361063

Keyword

nonn,cons

Author

Amiram Eldar, Mar 01 2023

Status

approved