A394334 - OEIS

%I #6 Mar 17 2026 09:58:07

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

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

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

%N Decimal expansion of the asymptotic mean of the number of exponential unitary divisors of the greatest common divisor of two positive integers selected independently at random.

%F Equals lim_{m->oo} (1/m^2) * Sum_{i,j=1..m} A278908(gcd(i, j)).

%F Equals Product_{p prime} (1-1/p^2)*(1 + Sum_{k >= 1} ud(k)/p^(2*k)), where ud(k) is the number of unitary divisors of k (A034444).

%e 1.078304786696831022734548475012806056531948835472367...

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

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

%Y Cf. A034444, A278908, A394333.

%K nonn,cons

%O 1,3

%A _Amiram Eldar_, Mar 17 2026