cp's OEIS Frontend

A271547 Decimal expansion of Product_{p prime} (1+1/(2p))*sqrt(1-1/p), a constant related to the asymptotic average number of squares modulo n.

%I A271547 #25 Mar 07 2025 01:28:26
%S A271547 8,1,2,1,0,5,7,1,1,1,6,3,1,2,2,5,1,1,7,0,6,2,5,0,9,6,4,5,8,1,8,8,7,1,
%T A271547 7,6,5,6,0,5,7,7,1,0,0,4,8,3,6,6,9,9,2,4,3,6,0,9,2,1,8,2,0,0,3,7,8,0,
%U A271547 9,4,0,6,2,0,4,2,5,3,2,2,0,7,5,5,8,0,2,5,4,0,2,3,5,0,4,0,2,9,9,8
%N A271547 Decimal expansion of Product_{p prime} (1+1/(2p))*sqrt(1-1/p), a constant related to the asymptotic average number of squares modulo n.
%H A271547 Steven R. Finch and Pascal Sebah, <a href="http://arXiv.org/abs/math.NT/0604465">Squares and Cubes Modulo n</a>, arXiv:math/0604465 [math.NT], 2006-2016.
%F A271547 Equals exp(Sum_{n>=2} -((-1)^n + 2^(n-1))*P(n)/(n*2^n)), where P(n) is the prime zeta P function.
%e A271547 0.81210571116312251170625096458188717656057710048366992436092182...
%t A271547 digits = 100; Exp[NSum[-( (-1)^n + 2^(n - 1))*PrimeZetaP[n]/(n* 2^n), {n, 2, Infinity}, NSumTerms -> 3 digits, WorkingPrecision -> digits + 10]] // RealDigits[#, 10, digits]& // First
%Y A271547 Cf. A046073, A105612.
%K A271547 nonn,cons
%O A271547 0,1
%A A271547 _Jean-François Alcover_, Apr 10 2016