A394002 - OEIS

%I #9 Jun 25 2026 00:44:07

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

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

%U 1,9,7,7,5,5,2,3,6,3,1,9,2,1,3,2,4,9,6,3,2,1,7,6,9,2,1,4,1,3,6,7,5,4,2,6,1

%N Decimal expansion of Product_{p prime} (1 - (3*p-1)/(p^2*(p+1))).

%C The asymptotic probability that two positive integers selected independently at random are coprime and both are exponentially odd numbers (A268335).

%F Equals A065463^2 * A394003.

%F Equals zeta(2) * A256392. - _Amiram Eldar_, Jun 24 2026

%e 0.358231630001961414567504290410102150117241844340819...

%o (PARI) prodeulerrat(1 - (3*p-1)/(p^2*(p+1)))

%Y Cf. A013661, A065463, A065473, A256392, A268335, A394003.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Mar 06 2026