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%I #16 Jan 12 2021 06:53:20
%S 1,0,5,6,1,8,2,1,2,1,7,2,6,8,1,6,1,4,1,7,3,7,9,3,0,7,6,5,3,1,6,2,1,9,
%T 8,9,0,5,8,7,5,8,0,4,2,5,4,6,0,7,0,8,0,1,2,0,0,4,3,0,6,1,9,8,3,0,2,7,
%U 9,2,8,1,6,0,6,2,2,2,6,9,3,0,4,8,9,5,1,2,9,5,8,3,7,2,9,1,5,9,7,1,8,4,7,5,0
%N Decimal expansion of the Product_{primes p == 1 (mod 4)} 1/(1-1/p^2).
%C The Euler product of the Riemann zeta function at 2 restricted to primes in A002144, which is the inverse of the infinite product (1-1/5^2)*(1-1/13^2)*(1-1/17^2)*(1-1/29^2)*...
%C There is a complementary Product_{primes p == 3 (mod 4)} 1/(1-1/p^2) = 1.16807558541051428866969673706404040136467... such that (this constant here)*1.16807.../(1-1/2^2) = zeta(2) = A013661.
%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 1/A088539. - _Vaclav Kotesovec_, May 05 2020
%F From _Amiram Eldar_, Sep 27 2020: (Start)
%F Equals Sum_{k>=1} 1/A004613(k)^2.
%F The complementary product equals Sum_{k>=1} 1/A004614(k)^2. (End)
%e 1.0561821217268161417379307653162198905...
%t digits = 105;
%t LandauRamanujanK = 1/Sqrt[2]*NProduct[((1 - 2^(-2^n))*Zeta[2^n]/ DirichletBeta[2^n])^(1/2^(n+1)), {n, 1, 24}, WorkingPrecision -> digits+5];
%t RealDigits[1/(4*LandauRamanujanK/Pi)^2, 10, digits][[1]] (* _Jean-François Alcover_, Jan 12 2021 *)
%Y Cf. A004613, A004614, A013661, A175646.
%K cons,nonn
%O 1,3
%A _R. J. Mathar_, Aug 01 2010
%E More digits from _Vaclav Kotesovec_, Jun 27 2020
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