A393648 Decimal expansion of 45045/(691*Pi^4).

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

Offset

0,1

Comments

The asymptotic probability that the greatest common divisor of two positive integers selected independently at random is a powerful number (A001694).

Links

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

Formula

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

Equals zeta(4)*zeta(6)/(zeta(2)*zeta(12)).

Equals A182448 * A269404.

Example

0.669220218035102573944120292716876378608731308968358...

Mathematica

RealDigits[45045/(691*Pi^4), 10, 120][[1]]

Prog

(PARI) 45045/(691*Pi^4)

Crossrefs

Cf. A001694, A013661, A013662, A013664, A013670, A112526, A182448, A269404.

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), this constant (powerful), A393649 (cubefull), A393650 (3-smooth), A393651 (prime power), A393652 (perfect power).

Sequence in context: A200616 A019851 A155880 * A389990 A217852 A021603

Adjacent sequences: A393645 A393646 A393647 * A393649 A393650 A393651

Keyword

nonn,cons,easy

Author

Amiram Eldar, Feb 24 2026

Status

approved