A175618 - OEIS

%I #7 Dec 15 2020 03:41:11

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

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

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

%N Decimal expansion of product_{n>=2} (1-n^(-7)).

%H E. Weisstein, <a href="http://mathworld.wolfram.com/InfiniteProduct.html">Infinite Product</a>, Mathworld.

%F Equals 1/product_{t=1..6} Gamma(2-exp(2*Pi*i*t/7)), where i is the imaginary unit and 2*Pi/7 = A019695.

%F Equals exp(Sum_{j>=1} (1 - zeta(7*j))/j). - _Vaclav Kotesovec_, Dec 15 2020

%e 0.99165495...

%t N[1/(7*Product[ Gamma[(-1)^(8*k/7 + 1)], {k, 1, 6}]), 105] // Re // RealDigits // First (* _Jean-François Alcover_, Feb 05 2013 *)

%o (PARI) exp(suminf(j=1, (1 - zeta(7*j))/j)) \\ _Vaclav Kotesovec_, Dec 15 2020

%Y Cf. A109219, A175615, A144666.

%K cons,easy,nonn

%O 0,1

%A _R. J. Mathar_, Jul 26 2010