

A192265


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


2



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
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OFFSET

1,3


COMMENTS

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


LINKS

Table of n, a(n) for n=1..86.


EXAMPLE

1.137470888095255613739630628948487638416238886570549395392900486463...


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[n100], n = n+100]; s[n] (* JeanFrançois Alcover, Feb 13 2013 *)


PROG

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


CROSSREFS

Cf. A192266.
Sequence in context: A193625 A198886 A305202 * A274511 A179706 A231325
Adjacent sequences: A192262 A192263 A192264 * A192266 A192267 A192268


KEYWORD

nonn,cons


AUTHOR

Paolo P. Lava, Jun 27 2011


STATUS

approved



