A393950 - OEIS

%I #10 Mar 06 2026 08:32:52

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

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

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

%N Decimal expansion of (1/zeta(2))^2 * Product_{p prime} ((p/(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 is a squarefree number (A005117).

%F Equals Product_{p prime} (p+1)^2/(p*(p+2)) * A393948.

%e 0.945052375049293634227126119205471990868896735111605...

%o (PARI) c(m) = prodeulerrat((p/(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/zeta(2)^2}

%Y Cf. A005117, A013661, A077609, A098198, A227929.

%Y Analogous constants: A215267, A393891.

%Y The asymptotic probability that the greatest common infinitary divisor of two positive integers selected independently at random is: A065472 (square), A393948 (1), A393949 (prime), this constant (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