This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A109694 #30 Sep 03 2024 09:23:24
%S A109694 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,
%T A109694 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,
%U A109694 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
%N A109694 Decimal expansion of Sum_{n>=1} 1/sigma_2(n).
%F A109694 Product_p Sum_{k>=0} 1/sigma_2(p^k).
%e A109694 1.5378128918272561625386610027382683309193600494732235492961768965942633...
%t A109694 $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 *)
%o A109694 (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...
%Y A109694 Cf. A001157 (sigma_2), A064602.
%K A109694 cons,nonn
%O A109694 1,2
%A A109694 _Franklin T. Adams-Watters_, Aug 07 2005
%E A109694 More digits from _Vaclav Kotesovec_, Sep 19 2020