cp's OEIS Frontend

A335590 Decimal expansion of the sum of the reciprocals of the squares of the perfect powers > 1.

%I A335590 #18 Jan 28 2021 21:28:40
%S A335590 1,0,0,4,7,5,3,2,7,2,0,0,0,9,3,7,7,5,8,6,0,1,4,8,9,5,1,6,4,3,6,7,9,5,
%T A335590 0,3,8,9,3,0,2,8,8,3,9,9,2,4,7,2,4,4,8,9,4,5,6,1,9,2,9,4,0,6,1,0,6,3,
%U A335590 5,7,7,3,4,9,4,4,6,9,2,1,7,0,5,0,9,5,8,5,2,0,5,1,2,1,8,1,6,3,9,7,6,2,0,5,7
%N A335590 Decimal expansion of the sum of the reciprocals of the squares of the perfect powers > 1.
%F A335590 Equals Sum_{k>=2} 1/A001597(k)^2.
%F A335590 Equals Sum_{k>=2} mu(k)*(1 - zeta(2*k)). - _Amiram Eldar_, Jan 27 2021
%e A335590 Equals 1/4^2 + 1/8^2 + 1/9^2 + 1/16^2 + 1/25^2 + 1/27^2 + 1/32^2 + 1/36^2 + 1/49^2 + 1/64^2 + 1/81^2 + 1/100^2 + ... = 0.10047532720009377586014895164367950389302883992472...
%t A335590 RealDigits[Sum[MoebiusMu[k]*(1 - Zeta[2*k]), {k, 2, 200}], 10, 105][[1]] (* _Amiram Eldar_, Jan 27 2021 *)
%o A335590 (PARI) suminf(k=2,moebius(k)*(1-zeta(2*k))) \\ _Hugo Pfoertner_, Jan 27 2021
%Y A335590 Cf. A001597, A013661, A085548, A275647, A335086, A335589, A340588.
%K A335590 nonn,cons
%O A335590 0,4
%A A335590 _Jon E. Schoenfield_, Jan 26 2021