A393651 Decimal expansion of (1/zeta(2)) * Sum_{p prime} 1/(p^2-1).

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

Offset

0,1

Comments

The asymptotic probability that the greatest common 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.

Formula

Equals A154945 / A013661.

Example

0.335389307556910373609942658316835328663268561577495...

Mathematica

$MaxExtraPrecision = 1000; Module[{m = 1000}, RealDigits[(1/Zeta[2]) * NSum[PrimeZetaP[n], {n, 2, m, 2}, NSumTerms -> m, WorkingPrecision -> m], 10, 105][[1]]]

Prog

(PARI) sumeulerrat(1/(p^2-1)) / zeta(2)

Crossrefs

Cf. A013661, A154945, A246655.

The asymptotic probability that the greatest common divisor of two positive integers selected at random is: A010701 (not 5-rough), A010722 (5-rough), A020773 (even), A059956 (1), A082020/10 (2), A152627 (odd), A182448 (square), A185197 (even power of 2), A215267 (squarefree), A217739 (power of 2), A222056 (prime), A343359 (cubefree), A393646 (cube), A393647 (exponentially odd number), A393648 (powerful), A393649 (cubefull), A393650 (3-smooth), this constant (prime power), A393652 (perfect power).

Sequence in context: A351561 A384911 A029620 * A204100 A048691 A332730

Adjacent sequences: A393648 A393649 A393650 * A393652 A393653 A393654

Keyword

nonn,cons

Author

Amiram Eldar, Feb 24 2026

Status

approved