A192265 Decimal expansion of Sum{k=1..infinity}{1/k^sigma(k)}.

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

Offset: 1

Author

Paolo P. Lava, Jun 27 2011

Keywords

• nonn
• cons

Comments

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

Examples

			1.137470888095255613739630628948487638416238886570549395392900486463...
		

Crossrefs

Cf. A192266.

Programs

Maple

with(numtheory);
P:=proc(i)
local a, n;
a:=0;
for n from 1 by 1 to i do a:=a+1/n^sigma(n); od;
print(evalf(a,300));
end:
P(1000);

Mathematica

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 *)

PARI

suminf(k=1,k^-sigma(k)) \\ Charles R Greathouse IV, Jun 29 2011