1,3

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.

R. J. Mathar, Table of Dirichlet L-series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], 2010-2015.

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

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

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).

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

1.1545383304763889439221065945555168298987751974487...

Cf. A000040, A001481, A055025.

Cf. A344123, A344125.

Sequence in context: A131291 A305394 A361803 * A237577 A131369 A122219

Adjacent sequences: A344121 A344122 A344123 * A344125 A344126 A344127

nonn,cons,more

A.H.M. Smeets, May 09 2021

approved