A394711 Decimal expansion of the asymptotic probability that two positive integers selected independently at random are coprime and both are nonsquarefree numbers.

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

Offset

0,2

Links

Table of n, a(n) for n=0..105.

Formula

Equals 6/Pi^2 - 2 * Product_{p prime} (1 - 2/p^2 + 1/p^3) + Product_{p prime} (1 - 3/p^2 + 2/p^3) = A059956 - 2 * A065464 + A065473.

Equals A229099^2 * A394712.

Example

0.038175518934316482333638076884557187617887465418664...

Prog

(PARI) 6/Pi^2 - 2 * prodeulerrat(1 - 2/p^2 + 1/p^3) + prodeulerrat(1 - 3/p^2 + 2/p^3)

Crossrefs

Cf. A013929, A059956, A065464, A065473, A229099, A394712.

Sequence in context: A054399 A013676 A199270 * A131563 A016622 A143623

Adjacent sequences: A394708 A394709 A394710 * A394712 A394713 A394714

Keyword

nonn,cons

Author

Amiram Eldar, Mar 30 2026

Status

approved