A334064 Decimal expansion of Sum_{k>=1} 1/sigma_3(k).

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

Offset

1,3

Links

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

Formula

Product_p Sum_{k>=0} 1/sigma_3(p^k).

Example

1.183473506178851103857342368295209694536571021407175977168478853541741442...

Mathematica

$MaxExtraPrecision = 1000; Do[Clear[f]; f[p_] := (1 + Sum[(p^3 - 1)/(p^(3 e + 3) - 1), {e, 1, emax}]); m = 1000; cc = Rest[CoefficientList[Series[Log[f[1/x]], {x, 0, m+3}], x]]; Print[f[2]*Exp[N[Sum[Indexed[cc, n]*(PrimeZetaP[n] - 1/2^n), {n, 2, m}], 120]]], {emax, 100, 400, 100}]

Crossrefs

Cf. A001158, A064603, A109694.

Sequence in context: A111436 A014549 A346441 * A021549 A013665 A209059

Adjacent sequences: A334061 A334062 A334063 * A334065 A334066 A334067

Keyword

nonn,cons

Author

Vaclav Kotesovec, Sep 19 2020

Status

approved