A394040 - OEIS

%I #6 Mar 08 2026 10:27:26

%S 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,

%T 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,

%U 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

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

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

%F Equals A185380 * A065472.

%F Equals zeta(2)^2 * A394039.

%e 0.204578804769207444392586756200127692571398462087897...

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

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

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Mar 08 2026