A335590 - OEIS

%I #18 Jan 28 2021 21:28:40

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

%F Equals Sum_{k>=2} 1/A001597(k)^2.

%F Equals Sum_{k>=2} mu(k)*(1 - zeta(2*k)). - _Amiram Eldar_, Jan 27 2021

%e 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 RealDigits[Sum[MoebiusMu[k]*(1 - Zeta[2*k]), {k, 2, 200}], 10, 105][[1]] (* _Amiram Eldar_, Jan 27 2021 *)

%o (PARI) suminf(k=2,moebius(k)*(1-zeta(2*k))) \\ _Hugo Pfoertner_, Jan 27 2021

%Y Cf. A001597, A013661, A085548, A275647, A335086, A335589, A340588.

%K nonn,cons

%O 0,4

%A _Jon E. Schoenfield_, Jan 26 2021