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Decimal expansion of Product_{k>=1} (1 + 1/A002476(k)^2).
4

%I #19 Aug 25 2021 12:59:54

%S 1,0,3,3,5,3,7,8,8,8,4,6,1,3,5,2,8,4,3,0,8,2,8,4,6,1,8,4,9,7,6,2,1,8,

%T 3,3,9,4,7,5,1,7,6,7,7,4,8,1,4,9,1,6,3,0,1,2,3,2,4,8,9,2,5,1,0,3,2,7,

%U 7,7,7,4,2,3,9,4,0,7,0,3,6,1,5,8,7,5,3,2,0,5,9,1,7,2,4,0,8,1,4,0,1,1,7,3,9

%N Decimal expansion of Product_{k>=1} (1 + 1/A002476(k)^2).

%C Product_{k>=1} (1 - 1/A002476(k)^2) = 1/A175646 = 0.9671040753637981066150556834173635260473412207450...

%C Let Zeta_{6,1}(4) = 1/ Product_{k>=1}(1-1/A002476(k)^4) = 1.0004615089.. and Zeta_{6,1}(2)= A175646 as tabulated in arXiv:1008.2547. Then this constant equals Zeta_{6,1}(2)/Zeta_{6,1}(4). - _R. J. Mathar_, Jan 12 2021

%H R. J. Mathar, <a href="https://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, Zeta_{6,1}(4) and Zeta_{6,1}(2) in Section 3.2.

%F A334481 * A334482 = 54/(5*Pi^2).

%e 1.03353788846135284308284618497621833947517677481...

%Y Cf. A002476, A175646, A334477, A334482.

%K nonn,cons

%O 1,3

%A _Vaclav Kotesovec_, May 02 2020

%E More digits from _Vaclav Kotesovec_, Jun 27 2020