A394334 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.

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, 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, 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

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} A278908(gcd(i, j)).

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).

Example

1.078304786696831022734548475012806056531948835472367...

Prog

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

Crossrefs

Cf. A034444, A278908, A394333.

Sequence in context: A245758 A266566 A309523 * A153622 A257576 A378129

Adjacent sequences: A394331 A394332 A394333 * A394335 A394336 A394337

Keyword

nonn,cons

Author

Amiram Eldar, Mar 17 2026

Status

approved