A394333 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.

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, 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, 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

Offset

1,3

Links

Table of n, a(n) for n=1..105.

Formula

Equals lim_{m->oo} (1/m^2) * Sum_{i,j=1..m} A049419(gcd(i, j)).

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).

Example

1.081450838371508794530463180241531998204014076074656...

Prog

(PARI) c(m) = prodeulerrat((1-1/p^2) * (1 + sum(k = 1, m, numdiv(k)/p^(2*k))));
{my(c1 = 0, c2 = 1, m = 2); while(c2 != c1, c1 = c2; c2 = c(m); m *= 2); c2}

Crossrefs

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

Sequence in context: A019981 A194281 A117038 * A365935 A172168 A373165

Adjacent sequences: A394330 A394331 A394332 * A394334 A394335 A394336

Keyword

nonn,cons

Author

Amiram Eldar, Mar 17 2026

Status

approved