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Decimal expansion of sum(1/k^(phi(k)), k=1..infinity), where phi(n) is the Euler totient function.
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%I #13 Dec 25 2023 17:41:35

%S 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,

%T 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,

%U 2,1,7,6,3,5,5,1,2,0,5,6,4,3,4,7,7,9,0

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

%C Rational approximation: 29329/17218.

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

%e 1.70339179928153054530520483941958492888306265194505541291458253107862176...

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

%Y Cf. A000010, A192265, A192266.

%K nonn,cons

%O 1,2

%A _Paolo P. Lava_, Mar 25 2014