A393948 Decimal expansion of Product_{p prime} ((1-1/p)^2 * Product_{k>=0} (1 + 2/p^(2^k))).

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

Offset

0,1

Comments

The asymptotic probability that the greatest common infinitary divisor of two positive integers selected independently at random equals 1 (i.e., they are infinitarily coprime).

Links

Table of n, a(n) for n=0..104.

Formula

Equals 2*A327576. - Artur Jasinski, Mar 04 2026

Example

0.733250553890763819113065441374003126067224311942018...

Prog

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

Crossrefs

Cf. A064380, A077609, A327576.

Analogous constants: A059956, A306071.

The asymptotic probability that the greatest common infinitary divisor of two positive integers selected independently at random is: A065472 (square), this constant (1), A393949 (prime), A393950 (squarefree), A393951 (Fermi-Dirac prime), A393952 (exponentially 2^n-number), A393953 (4th power).

Sequence in context: A135041 A021581 A265411 * A380010 A176833 A154019

Adjacent sequences: A393945 A393946 A393947 * A393949 A393950 A393951

Keyword

nonn,cons

Author

Amiram Eldar, Mar 04 2026

Status

approved