A192265 - OEIS

%I #14 May 13 2013 01:49:39

%S 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 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 3,4,0,6,2,5,8,0,5,2,0,4,1,0,1,7,3,2

%N Decimal expansion of Sum{k=1..infinity}{1/k^sigma(k)}

%C Rational approximation: 18071/15887. Continued fraction (1,7,3,1,1,1,4,1,2,1,2,3...).

%e 1.137470888095255613739630628948487638416238886570549395392900486463...

%p with(numtheory);

%p P:=proc(i)

%p local a, n;

%p a:=0;

%p for n from 1 by 1 to i do a:=a+1/n^sigma(n); od;

%p print(evalf(a,300));

%p end:

%p P(1000);

%t 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 (PARI) suminf(k=1,k^-sigma(k)) \\ _Charles R Greathouse IV_, Jun 29 2011

%Y Cf. A192266.

%K nonn,cons

%O 1,3

%A _Paolo P. Lava_, Jun 27 2011