A394007 - OEIS

%I #4 Mar 06 2026 14:49:54

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

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

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

%N Decimal expansion of zeta(3)^2 * Product_{p prime} (1 - 1/p^2 - 2/p^3 + 2/p^4).

%C The asymptotic probability that two cubefree numbers selected independently at random are coprime.

%F Equals zeta(3)^2 * A394006.

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

%e 0.676360626983496754089102877222555507544109873453869...

%o (PARI) zeta(3)^2 * prodeulerrat(1 - 1/p^2 - 2/p^3 + 2/p^4)

%Y Cf. A002117, A004709, A065472, A088453, A394006.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Mar 06 2026