A394286 Decimal expansion of Product_{p prime} (1 - 2/(p^2*(p+1))).

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

Offset

0,1

Comments

The asymptotic probability that the greatest common divisor of two positive integers selected independently at random equals their greatest common unitary divisor.

In other words, for all primes p, if these two integers are both divisible by p, then they have equal p-adic valuations (exponents of p in their prime factorizations).

The asymptotic density of A398161. - Amiram Eldar, Jul 22 2026

Links

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

Teerapat Srichan, Nithi Rungtanapirom, and Saeree Wananiyakul, On the distribution of consecutive M-free integers, RAIRO - Theoretical Informatics and Applications, Vol. 60 (2026), Article 22.

Formula

Equals zeta(2) * Product_{p prime} (1 - 1/p^2 - 2/p^3 + 2/p^4) = A013661 * A394006.

Equals (1/zeta(2)) * Product_{p prime} (1 + 1/(p+1)^2) = A059956 * A065486.

Example

0.769975239128165285596843943228823906161378619145338...

Prog

(PARI) prodeulerrat(1 - 2/(p^2*(p+1)))

Crossrefs

Cf. A013661, A059956, A065486, A077610, A394006, A394287, A398161.

Sequence in context: A021569 A085964 A383647 * A281313 A082121 A309622

Adjacent sequences: A394283 A394284 A394285 * A394287 A394288 A394289

Keyword

nonn,cons,changed

Author

Amiram Eldar, Mar 15 2026

Status

approved