A361059 Decimal expansion of the asymptotic mean of A000005(k)/A286324(k), the ratio between the number of divisors and the number of bi-unitary divisors.

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

Offset: 1

Author

Amiram Eldar, Mar 01 2023

Keywords

• nonn
• cons

Examples

			1.158854572650312100164480196393175149039104318857395...
		

Links

• Eric Weisstein's World of Mathematics, Biunitary Divisor.

Crossrefs

Cf. A000005, A286324, A361060 (mean of the inverse ratio).

Cf. A307869 (unitary analog), A308043.

Programs

Mathematica

$MaxExtraPrecision = 1000; m = 1000; f[p_] := 1 - (p - 1)*Log[1 - 1/p^2]/(2*p); 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, 106][[1]]

Formula

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

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