A109694 Decimal expansion of Sum_{n>=1} 1/sigma_2(n).

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

Offset: 1

Author

Franklin T. Adams-Watters, Aug 07 2005

Keywords

• cons
• nonn

Examples

			1.5378128918272561625386610027382683309193600494732235492961768965942633...
		

Crossrefs

Cf. A001157 (sigma_2), A064602.

Programs

Mathematica

$MaxExtraPrecision = 1000; Do[Clear[f]; f[p_] := (1 + Sum[(p^2 - 1)/(p^(2*e + 2) - 1), {e, 1, emax}]); m = 1000; cc = Rest[CoefficientList[Series[Log[f[1/x]], {x, 0, m}], x]]; Print[f[2]*Exp[N[Sum[cc[[n]] * (PrimeZetaP[n] - 1/2^n), {n, 2, m}], 120]]], {emax, 100, 400, 100}] (* Vaclav Kotesovec, Sep 19 2020 *)

PARI

N=10^9; prodeuler(p=2,N, sum(k=1,200/log(p),if(k==1,1.,1./((p^(2*k)-1)/(p^2-1))))) \\ The output is 1.537812891756...

Formula

Product_p Sum_{k>=0} 1/sigma_2(p^k).

Extensions

More digits from Vaclav Kotesovec, Sep 19 2020