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A361013
Decimal expansion of a constant related to the asymptotics of A361012.
5
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
1,1
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
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Feb 28 2023
STATUS
approved