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 A192265 #16 Jun 02 2025 04:11:33
%S A192265 1,1,3,7,4,7,0,8,8,8,0,9,5,2,5,5,6,1,3,7,3,9,6,3,0,6,2,8,9,4,8,4,8,7,
%T A192265 6,3,8,4,1,6,2,3,8,8,8,6,5,7,0,5,4,9,3,9,5,3,9,2,9,0,0,4,8,6,4,6,3,3,
%U A192265 3,4,0,6,2,5,8,0,5,2,0,4,1,0,1,7,3,2
%N A192265 Decimal expansion of Sum{k=1..infinity}{1/k^sigma(k)}.
%C A192265 Rational approximation: 18071/15887. Continued fraction (1,7,3,1,1,1,4,1,2,1,2,3...).
%e A192265 1.137470888095255613739630628948487638416238886570549395392900486463...
%p A192265 with(numtheory);
%p A192265 P:=proc(i)
%p A192265 local a, n;
%p A192265 a:=0;
%p A192265 for n from 1 by 1 to i do a:=a+1/n^sigma(n); od;
%p A192265 print(evalf(a,300));
%p A192265 end:
%p A192265 P(1000);
%t A192265 Clear[s]; s[n_] := s[n] = RealDigits[ Sum[ 1/k^DivisorSigma[1, k], {k, 1, n}], 10, 86] // First; s[n=100]; While[s[n] != s[n-100], n = n+100]; s[n] (* _Jean-François Alcover_, Feb 13 2013 *)
%o A192265 (PARI) suminf(k=1,k^-sigma(k)) \\ _Charles R Greathouse IV_, Jun 29 2011
%Y A192265 Cf. A192266.
%K A192265 nonn,cons
%O A192265 1,3
%A A192265 _Paolo P. Lava_, Jun 27 2011