A394042 Decimal expansion of Product_{p prime} (1 - 2/p^3 - 1/p^4 + 2/p^5).

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

Offset

0,1

Comments

The asymptotic probability that two positive integers selected independently at random are both cubefree numbers (A004709), and their greatest common divisor is a squarefree number (A005117).

Links

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

Formula

Equals (1/zeta(2)) * Product_{p prime} (1 + 1/p^2 - 2/p^3) = A059956 * A330594.

Equals A394041 / zeta(3)^2.

Example

0.672951052727728482264636640701335995948024437122073...

Prog

(PARI) prodeulerrat(1 - 2/p^3 - 1/p^4 + 2/p^5)

Crossrefs

Cf. A002117, A004709, A005117, A013661, A059956, A183030, A330594, A394041, A394044.

Sequence in context: A316165 A267251 A378351 * A259526 A108664 A160155

Adjacent sequences: A394039 A394040 A394041 * A394043 A394044 A394045

Keyword

nonn,cons

Author

Amiram Eldar, Mar 08 2026

Status

approved