A393948 - OEIS

%I #15 Mar 06 2026 08:33:23

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

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

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

%N Decimal expansion of Product_{p prime} ((1-1/p)^2 * Product_{k>=0} (1 + 2/p^(2^k))).

%C The asymptotic probability that the greatest common infinitary divisor of two positive integers selected independently at random equals 1 (i.e., they are infinitarily coprime).

%F Equals 2*A327576. - _Artur Jasinski_, Mar 04 2026

%e 0.733250553890763819113065441374003126067224311942018...

%o (PARI) c(m) = prodeulerrat((1 - 1/p)^2 * prod(k = 0, m, 1 + 2/p^(2^k)));

%o {my(c1 = 0, c2 = 1, m = 1); while(c2 != c1, c1 = c2; c2 = c(m); m++); c2}

%Y Cf. A064380, A077609, A327576.

%Y Analogous constants: A059956, A306071.

%Y The asymptotic probability that the greatest common infinitary divisor of two positive integers selected independently at random is: A065472 (square), this constant (1), A393949 (prime), A393950 (squarefree), A393951 (Fermi-Dirac prime), A393952 (exponentially 2^n-number), A393953 (4th power).

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Mar 04 2026