A192266 -id:A192266 - cp's OEIS frontend

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

Paolo P. Lava, Jun 27 2011

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

			1.137470888095255613739630628948487638416238886570549395392900486463...

Cf. A192266.

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);

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 *)

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

A239725 Decimal expansion of sum(1/k^(phi(k)), k=1..infinity), where phi(n) is the Euler totient function.

Original entry on oeis.org

1, 7, 0, 3, 3, 9, 1, 7, 9, 9, 2, 8, 1, 5, 3, 0, 5, 4, 5, 3, 0, 5, 2, 0, 4, 8, 3, 9, 4, 1, 9, 5, 8, 4, 9, 2, 8, 8, 8, 3, 0, 6, 2, 6, 5, 1, 9, 4, 5, 0, 5, 5, 4, 1, 2, 9, 1, 4, 5, 8, 2, 5, 3, 1, 0, 7, 8, 6, 2, 1, 7, 6, 3, 5, 5, 1, 2, 0, 5, 6, 4, 3, 4, 7, 7, 9, 0

Offset: 1

Paolo P. Lava, Mar 25 2014

Rational approximation: 29329/17218.

Continued fraction: (1, 1, 2, 2, 1, 2, 4, 36, 3, 1, 11, …).

			1.70339179928153054530520483941958492888306265194505541291458253107862176...

Cf. A000010, A192265, A192266.

with(numtheory); P:=proc(q) local k; print(evalf(add(1/k^phi(k),k=1..q),100)); end: P(1000);

cp's OEIS Frontend

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

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