A335086 - OEIS

%I #46 Dec 03 2022 05:42:40

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

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

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

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

%F Equals Sum_{k>=1} 1/(A106543(k)^2).

%F Equals zeta(2) - P(2) - 1 - Sum_{k>=2} mu(k)*(1-zeta(2*k)), where P(s) is the prime zeta function. - _Amiram Eldar_, Dec 03 2022

%e Equals 1/(6^2) + 1/(10^2) + 1/(12^2) + 1/(14^2) + ... = 0.092211319607067162105722850170097751152689718042181...

%t perfPQ[n_] := GCD @@ FactorInteger[n][[All, 2]] > 1

%t scdc[n_] := 1/(Select[Range[n, n], CompositeQ[#] && ! perfPQ[#] &])

%t N[Total[ParallelTable[scdc[k]^2, {k, 2, 10^8}] /. {} -> Sequence[]], 100]

%o (Sage)

%o sum_A335086 = (i for i in NN if i>3 and not i.is_prime() and not i.is_perfect_power())

%o s = RLF(0); s

%o RealField(110)(s)

%o for i in range(0, 5000000): s += 1 / next(sum_A335086)^2

%o print(s) #

%Y Cf. A106543.

%Y Cf. A013661, A085548.

%K nonn,cons

%O -1,1

%A _Terry D. Grant_, Sep 11 2020

%E a(7)-a(16) from _Jinyuan Wang_, Nov 07 2020

%E More digits from _Jon E. Schoenfield_, Jan 26 2021