A394715 Decimal expansion of (1/zeta(4)) * Sum_{p prime} 1/(p^4-1).

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

Offset

0,2

Comments

The asymptotic probability that the greatest common square divisor of two positive integers selected independently at random is a prime power (not including 1, i.e., A056798 \ {1}).

Links

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

Formula

Equals (1/zeta(4)) * Sum_{k>=1} P(4*k), where P is the prime zeta function.

Example

0.0751317800794047337553663344221169780971903740559052...

Prog

(PARI) sumeulerrat(1/(p^4-1)) / zeta(4)

Crossrefs

Cf. A013662, A056798, A393651, A393899.

Sequence in context: A254177 A377609 A021575 * A334632 A154870 A098687

Adjacent sequences: A394712 A394713 A394714 * A394716 A394717 A394718

Keyword

nonn,cons

Author

Amiram Eldar, Mar 30 2026

Status

approved