A394254 - OEIS

%I #5 Mar 14 2026 09:43:25

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

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

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

%N Decimal expansion of the asymptotic mean of the number of common infinitary divisors of two positive integers selected independently at random.

%F Equals lim_{m->oo} (1/m)^2 * Sum_{i,j=1..m} A037445(gcid(i, j)), where gcid is the greatest common infinitary divisor function.

%F Equals Product_{p prime, k>=0} (1 + 1/(p^(2^k) + 1)^2).

%e 1.337901945280194785191226984116163054005489381027493...

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

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

%Y Cf. A037445.

%Y Cf. A013661, A065486, A082020, A394253.

%K nonn,cons

%O 1,2

%A _Amiram Eldar_, Mar 14 2026