A361013 Decimal expansion of a constant related to the asymptotics of A361012.

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

Offset: 1

Author

Vaclav Kotesovec, Feb 28 2023

Keywords

• nonn
• cons

Examples

			2.960080302024941410481820478110894693928439095925163411967504480866339...
		

Crossrefs

Cf. A361012, A327837, A327838.

Programs

Mathematica

$MaxExtraPrecision = 1000; smax = 500; Do[Clear[f]; f[p_] := 1 + Sum[(DivisorSigma[1, e] - DivisorSigma[1, e-1])/p^e, {e, 2, emax}]; cc = Rest[CoefficientList[Series[Log[f[1/x]], {x, 0, smax}], x, smax + 1]]; Print[f[2] * f[3] * f[5] * f[7] * Exp[N[Sum[cc[[n]]*(PrimeZetaP[n] - 1/2^n - 1/3^n - 1/5^n - 1/7^n), {n, 2, smax}], 120]]], {emax, 100, 1000, 100}]

Formula

Equals limit_{n->oo} A361012(n) / n.

Equals Product_{p prime} (1 + Sum_{e>=2} (sigma(e) - sigma(e-1)) / p^e), where sigma = A000203.