%I #14 Sep 18 2022 14:31:03
%S 5,5,9,2,2,8,6,8,0,7,1,2,4,2,8,0,4,2,4,2,5,4,3,4,3,3,6,7,0,3,9,8,2,0,
%T 6,7,4,8,6,5,6,5,3,6,1,2,4,2,4,2,8,2,7,3,1,6,5,9,0,0,8,9,1,0,2,5,6,6,
%U 6,2,2,6,3,7,6,2,9,4,6,0,9,0,0,4,8,5,4
%N Decimal expansion of Sum_{n>=2} (-1)^n/(n*phi(n)), where phi(n) is the Euler totient function A000010.
%C The formula section of A000010 provides the following conjecture: Sum_{i>=2} (-1)^i/(i*phi(i)) exists and is approximately 0.558. - Orges Leka (oleka(AT)students.uni-mainz.de), Dec 23 2004
%C A more accurate value of the conjectured limit is provided.
%F Equals 1 - (1/5) * A065484. - _Amiram Eldar_, Nov 11 2020
%e 0.5592286807124280424254343367039820674865653612424...
%o (PARI) 1 - prodeulerrat(1 + p/((p-1)^2*(p+1)))/5 \\ _Amiram Eldar_, Nov 11 2020
%Y Cf. A000010, A002618, A065484.
%K nonn,cons
%O 0,1
%A _Hugo Pfoertner_, May 31 2020
%E More terms from _Amiram Eldar_, Nov 11 2020