A394254 Decimal expansion of the asymptotic mean of the number of common infinitary divisors of two positive integers selected independently at random.

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

Offset

1,2

Links

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

Formula

Equals lim_{m->oo} (1/m)^2 * Sum_{i,j=1..m} A037445(gcid(i, j)), where gcid is the greatest common infinitary divisor function.

Equals Product_{p prime, k>=0} (1 + 1/(p^(2^k) + 1)^2).

Example

1.337901945280194785191226984116163054005489381027493...

Prog

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

Crossrefs

Cf. A037445.

Cf. A013661, A065486, A082020, A394253.

Sequence in context: A288728 A213942 A144554 * A177936 A337975 A143088

Adjacent sequences: A394251 A394252 A394253 * A394255 A394256 A394257

Keyword

nonn,cons

Author

Amiram Eldar, Mar 14 2026

Status

approved