A394333 - OEIS

%I #11 Mar 21 2026 09:38:30

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

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

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

%N Decimal expansion of the asymptotic mean of the number of exponential 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} A049419(gcd(i, j)).

%F Equals Product_{p prime} (1-1/p^2)*(1 + Sum_{k >= 1} d(k)/p^(2*k)), where d(k) is the number of divisors of k (A000005).

%e 1.081450838371508794530463180241531998204014076074656...

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

%o {my(c1 = 0, c2 = 1, m = 2); while(c2 != c1, c1 = c2; c2 = c(m); m *= 2); c2}

%Y Cf. A000005, A049419, A322791, A327837, A394334.

%K nonn,cons

%O 1,3

%A _Amiram Eldar_, Mar 17 2026