cp's OEIS Frontend

A334480 Decimal expansion of Product_{k>=1} (1 - 1/A007528(k)^3).

%I A334480 #20 Aug 25 2021 12:59:25
%S A334480 9,9,0,8,8,4,1,4,5,5,2,5,2,1,3,3,5,6,5,6,3,4,0,3,1,7,3,5,5,9,4,3,2,7,
%T A334480 5,1,6,4,3,4,8,3,1,2,1,7,5,0,0,7,6,1,3,3,0,4,8,6,7,7,4,7,8,4,9,4,3,1,
%U A334480 7,8,8,8,2,5,7,6,7,4,3,1,7,7,5,2,7,6,3,4,5,2,1,7,8,9,8,8,9,2,9,2,1,3,5,4,6,7
%N A334480 Decimal expansion of Product_{k>=1} (1 - 1/A007528(k)^3).
%C A334480 In general, for s > 0, Product_{k>=1} (1 + 1/A007528(k)^(2*s+1)) / (1 - 1/A007528(k)^(2*s+1)) = (1 - 1/2^(2*s + 1)) * (3^(2*s + 1) - 1) * (2*s)! * zeta(2*s + 1) / (sqrt(3) * A002114(s) * Pi^(2*s + 1)).
%C A334480 For s > 1, Product_{k>=1} (1 + 1/A007528(k)^s) / (1 - 1/A007528(k)^s) = (2^s - 1) * (3^s - 1) * zeta(s) / (zeta(s, 1/6) - zeta(s, 5/6)).
%C A334480 For s > 1, Product_{k>=1} (1 - 1/A002476(k)^s) * (1 - 1/A007528(k)^s) = 6^s / ((2^s - 1)*(3^s - 1)*zeta(s)).
%H A334480 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, p. 26 (case 6 5 3 = 1/A334480).
%F A334480 A334479 / A334480 = 91*sqrt(3)*zeta(3)/(6*Pi^3).
%F A334480 A334478 * A334480 = 108/(91*zeta(3)).
%e A334480 0.990884145525213356563403173559432751643483121750... = 1/1.0091997177631243951237...
%Y A334480 Cf. A007528, A175646, A334425, A334427, A334479.
%K A334480 nonn,cons
%O A334480 0,1
%A A334480 _Vaclav Kotesovec_, May 02 2020
%E A334480 More digits from _Vaclav Kotesovec_, Jun 27 2020