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%I #23 Oct 26 2020 22:51:48
%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
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