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A361013 revision #9

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

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OFFSET

1,1

LINKS

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

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.

EXAMPLE

2.960080302024941410481820478110894693928439095925163411967504480866339...

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}]

CROSSREFS

Cf. A361012, A327837, A327838.

Sequence in context: A069857 A076841 A213819 * A193088 A162916 A057273

Adjacent sequences: A361010 A361011 A361012 * A361014 A361015 A361016

KEYWORD

nonn,cons

AUTHOR

Vaclav Kotesovec, Feb 28 2023

STATUS

reviewed