A393891 Decimal expansion of Product_{p prime} (1 - (p-1)/(p^4*(p+1))).

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

Offset

0,1

Comments

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

Links

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

Formula

Equals zeta(2) * Product_{p prime} (1 - 1/p^2 - 1/p^4 + 2/p^5 - 1/p^6).

Example

0.971672001840052390434359835667018698919523514310257...

Prog

(PARI) prodeulerrat(1 - (p-1)/(p^4*(p+1)))

Crossrefs

Cf. A005117, A013661, A077610, A215267.

The asymptotic probability that the greatest common unitary divisor of two positive integers selected at random is: A021016 (even), A306071 (1), this constant (squarefree), A393892 (cubefree), A393893 (powerful), A393894 (cubefull), A393895 (square), A393896 (cube), A393897 (exponentially odd number), A393898 (prime), A393899 (prime power), A393900 (perfect power).

Sequence in context: A389016 A309570 A383860 * A254249 A393374 A298752

Adjacent sequences: A393888 A393889 A393890 * A393892 A393893 A393894

Keyword

nonn,cons

Author

Amiram Eldar, Mar 02 2026

Status

approved