cp's OEIS Frontend

A344123 Decimal expansion of Sum_{i > 0} 1/A001481(i)^2.

%I A344123 #18 Aug 25 2021 13:04:23
%S A344123 1,4,2,6,5,5,6,0,6,3,5,1,2,5,9,2,8,7,8,6,9,6,8,0,9,3,1,6,1,5,5,0,8,1,
%T A344123 6,3,6,1,2,7,6,6,9,3,6,3,6,7,7,0,3,9,0,2,8,8,7,9,9,2,2,3,0,4,4,1,2,9,
%U A344123 6,0,4,5,2,8,6,1,5,1,9,0,1,9,1,4,6,7
%N A344123 Decimal expansion of Sum_{i > 0} 1/A001481(i)^2.
%C A344123 This constant can be considered as an equivalent of zeta(2) (= Pi^2/6 = A013661), where Euler's zeta(2) 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.
%C A344123 Close to the value of e^(3/2)/Pi.
%H A344123 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 A344123 Equals Sum_{i > 0} 1/A001481(i)^2.
%F A344123 Equals Product_{i > 0} 1/(1-A055025(i)^-2).
%F A344123 Equals 1/(1-prime(1)^(-2)) * Product_{i>1 and prime(i) == 1 (mod 4)} 1/(1-prime(i)^(-2)) * Product_{i>1 and prime(i) == 3 (mod 4)} 1/(1-prime(i)^(-4)), where prime(n) = A000040(n).
%F A344123 Equals (4/3)/(A243379*A334448).
%F A344123 Equals zeta_{2,0} (2) * zeta_{4,1} (2) * zeta_{4,3} (4), where zeta_{4,1} (2)  = A175647 and zeta_{2,0} (s) = 2^s/(2^s - 1).
%e A344123 1.4265560635125928786968093161550816361276693636770...
%Y A344123 Cf. A000040, A001481, A055025, A175647, A243379, A334448.
%Y A344123 Cf. A344124, A344125.
%K A344123 nonn,cons
%O A344123 1,2
%A A344123 _A.H.M. Smeets_, May 09 2021