A393950 Decimal expansion of (1/zeta(2))^2 * Product_{p prime} ((p/(p+2)) * Product_{k>=0} (1 + 2/p^(2^k))).

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

Offset

0,1

Comments

The asymptotic probability that the greatest common infinitary divisor of two positive integers selected independently at random is a squarefree number (A005117).

Links

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

Formula

Equals Product_{p prime} (p+1)^2/(p*(p+2)) * A393948.

Example

0.945052375049293634227126119205471990868896735111605...

Prog

(PARI) c(m) = prodeulerrat((p/(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/zeta(2)^2}

Crossrefs

Cf. A005117, A013661, A077609, A098198, A227929.

Analogous constants: A215267, A393891.

The asymptotic probability that the greatest common infinitary divisor of two positive integers selected independently at random is: A065472 (square), A393948 (1), A393949 (prime), this constant (squarefree), A393951 (Fermi-Dirac prime), A393952 (exponentially 2^n-number), A393953 (4th power).

Sequence in context: A393780 A344949 A300072 * A380334 A062546 A245887

Adjacent sequences: A393947 A393948 A393949 * A393951 A393952 A393953

Keyword

nonn,cons

Author

Amiram Eldar, Mar 04 2026

Status

approved