A337768 - OEIS

%I #26 Dec 21 2024 17:38:27

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

%T 1,1,0,8,7,4,4,9,5,2,3,4,2,8,1,7,0,1,8,5,5,0,4,9,4,0,8,9,5,3,1,0,4,4,

%U 1,8,7,2,7,6,2,1,3,0,2,0,2,7,5,5,8,7,7,9

%N Decimal expansion of the sum of reciprocals of squared composite numbers that are not prime powers.

%F Equals Sum_{k>=1} 1/(A024619(k)^2).

%F Equals zeta(2) - 1 - Sum_{k>1} P(2*k) = A013661 - 1 - A154945, where P is the prime zeta function. - _Amiram Eldar_, Sep 21 2020

%e Equals 1/(6^2) + 1/(10^2) + 1/(12^2) + 1/(14^2) + ... + = 0.0932407691912272520326841426746816110874495234281701855...

%t A337768[n_] := 1/Select[Range[n, n], ! PrimePowerQ[#] && CompositeQ[#] &] N[Total[ParallelTable[A337768[k]^2, {k, 2, 10^8}]/.{} -> Sequence[]], 62]

%o (Sage)

%o sum_A337768 = (i for i in NN if i>3 and not i.is_prime() and not i.is_prime_power())

%o s = RLF(0); s

%o RealField(110)(s)

%o for i in range(0, 5000000): s += 1 / next(sum_A337768)^2

%o print(s) #

%Y Cf. A013661, A024619, A154945.

%K nonn,cons

%O 0,2

%A _Terry D. Grant_, Sep 19 2020

%E More terms from _Amiram Eldar_, Sep 21 2020