%I #21 Aug 25 2021 13:00:38

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

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

%N Decimal expansion of Sum_{i > 0} 1/A001481(i)^3.

%C This constant can be considered as an analog of zeta(3) (= Apéry's constant = A002117), where Euler's zeta(3) is over all positive integers, with prime elements in A000040, while this constant is over all positive integers that can be written as the sum of two squares (A001481) with prime elements given in A055025.

%H R. J. Mathar, <a href="http://arxiv.org/abs/1008.2547">Table of Dirichlet L-series and Prime Zeta Modulo Functions for Small Moduli</a>, arXiv:1008.2547 [math.NT], 2010-2015.

%F Equals Sum_{i > 0} 1/A001481(i)^3.

%F Equals Product_{i > 0} 1/(1-A055025(i)^-3).

%F Equals 1/(1-prime(1)^(-3)) * Product_{i>1 and prime(i) == 1 (mod 4)} 1/(1-prime(i)^(-3)) * Product_{i>1 and prime(i) == 3 (mod 4)} 1/(1-prime(i)^(-6)), where prime(n) = A000040(n).

%F Equals zeta_{2,0} (3) * zeta_{4,1} (3) * zeta_{4,3} (6), where zeta_{2,0} (s) = 2^s/(2^s - 1).

%e 1.1545383304763889439221065945555168298987751974487...

%Y Cf. A000040, A001481, A055025.

%Y Cf. A344123, A344125.

%K nonn,cons,more

%O 1,3

%A _A.H.M. Smeets_, May 09 2021