# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a344124
Showing 1-1 of 1

%I A344124 #21 Aug 25 2021 13:00:38
%S A344124 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 A344124 8,2,9,8,9,8,7,7,5,1,9,7,4,4,8,7
%N A344124 Decimal expansion of Sum_{i > 0} 1/A001481(i)^3.
%C A344124 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 A344124 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 A344124 Equals Sum_{i > 0} 1/A001481(i)^3.
%F A344124 Equals Product_{i > 0} 1/(1-A055025(i)^-3).
%F A344124 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 A344124 Equals zeta_{2,0} (3) * zeta_{4,1} (3) * zeta_{4,3} (6), where zeta_{2,0} (s) = 2^s/(2^s - 1).
%e A344124 1.1545383304763889439221065945555168298987751974487...
%Y A344124 Cf. A000040, A001481, A055025.
%Y A344124 Cf. A344123, A344125.
%K A344124 nonn,cons,more
%O A344124 1,3
%A A344124 _A.H.M. Smeets_, May 09 2021

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE