A393899 Decimal expansion of Product_{p prime} (1 - (p-1)/(p^2*(p+1))) * Sum_{p prime} ((p-1)/(p^3 + p^2 - p +1)).

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

Offset

0,2

Comments

The asymptotic probability that the greatest common unitary divisor of two positive integers selected independently at random is a prime power (not including 1, i.e., A246655).

Links

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

Example

0.177710452714376703633900981683114429048352742926913...

Prog

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

Crossrefs

Cf. A077610, A246655, A393651.

The asymptotic probability that the greatest common unitary divisor of two positive integers selected at random is: A021016 (even), A306071 (1), A393891 (squarefree), A393892 (cubefree), A393893 (powerful), A393894 (cubefull), A393895 (square), A393896 (cube), A393897 (exponentially odd number), A393898 (prime), this constant (prime power), A393900 (perfect power).

Sequence in context: A397375 A382587 A022619 * A384625 A131685 A019860

Adjacent sequences: A393896 A393897 A393898 * A393900 A393901 A393902

Keyword

nonn,cons

Author

Amiram Eldar, Mar 02 2026

Status

approved