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%I #12 Jun 25 2023 01:52:12
%S 0,3,8,5,1,6,1,9,2,9,8,2,6,9,4,6,4,0,9,1,2,8,3,7,9,2,2,6,2,8,0,6,0,3,
%T 9,5,4,3,8,9,0,0,1,6,7,4,7,8,3,8,1,5,7,1,9,3,7,1,9,1,5,5,8,9,2,2,3,7,
%U 5,5,3,7,8,3,4,5,9,1,6,6,1,3,9,3,0,4,7,4,1,4,7,6,2,0,4,9,4,7,1,5,0,8,4,4,4
%N Decimal expansion of the sum of the reciprocals of squared 3-almost primes.
%C zeta(2) = A013661 is 1 plus a sum over inverse squares of k-almost primes, k=1 to infinity, where A085548 represents k=1, A117543 represents k=2 and this constant here represents k=3.
%H R. J. Mathar, <a href="http://arXiv.org/abs/0803.0900">Series of reciprocal powers of k-almost primes</a>, arXiv:0803.0900 [math.NT], 2008-2009.
%F Equals A085548^3 / 6 + A085966 / 3 + A085548 * A085964 / 2.
%F Equals Sum_{i>=1} 1/A000290(A014612(i)).
%e 0.038516192982694640912837922628060395438900167478381571937...
%t RealDigits[PrimeZetaP[2]^3/6 + PrimeZetaP[6]/3 + PrimeZetaP[2]*PrimeZetaP[4]/2, 10, 120, -1][[1]] (* _Amiram Eldar_, Jun 25 2023 *)
%Y Cf. A000290, A013661, A014612, A085548, A085964, A085966, A117543, A085548.
%K cons,nonn
%O 0,2
%A _R. J. Mathar_, Sep 10 2007, Mar 07 2008
%E a(104) corrected by _Amiram Eldar_, Jun 25 2023
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