A394040 Decimal expansion of Sum_{p prime} (1/(p*(p+2))) * Product_{p prime} (1 - 1/(p+1)^2).

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

Offset

0,1

Comments

The asymptotic probability that the greatest common divisor of two squarefree numbers selected independently at random is prime.

Links

Table of n, a(n) for n=0..106.

Formula

Equals A185380 * A065472.

Equals zeta(2)^2 * A394039.

Example

0.204578804769207444392586756200127692571398462087897...

Prog

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

Crossrefs

Cf. A005117, A013661, A065472, A098198, A185380, A227929, A394039.

Sequence in context: A385712 A068333 A378748 * A121451 A265820 A096984

Adjacent sequences: A394037 A394038 A394039 * A394041 A394042 A394043

Keyword

nonn,cons

Author

Amiram Eldar, Mar 08 2026

Status

approved