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

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, 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, 6, 0, 4, 5, 2, 8, 6, 1, 5, 1, 9, 0, 1, 9, 1, 4, 6, 7

Offset

1,2

Comments

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.

Close to the value of e^(3/2)/Pi.

Links

Table of n, a(n) for n=1..86.

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

Formula

Equals Sum_{i > 0} 1/A001481(i)^2.

Equals Product_{i > 0} 1/(1-A055025(i)^-2).

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).

Equals (4/3)/(A243379*A334448).

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).

Example

1.4265560635125928786968093161550816361276693636770...

Crossrefs

Cf. A000040, A001481, A055025, A175647, A243379, A334448.

Cf. A344124, A344125.

Sequence in context: A372529 A021705 A228084 * A188941 A200347 A135853

Adjacent sequences: A344120 A344121 A344122 * A344124 A344125 A344126

Keyword

nonn,cons

Author

A.H.M. Smeets, May 09 2021

Status

approved