A394711 - OEIS

%I #5 Mar 31 2026 00:05:44

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

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

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

%N Decimal expansion of the asymptotic probability that two positive integers selected independently at random are coprime and both are nonsquarefree numbers.

%F Equals 6/Pi^2 - 2 * Product_{p prime} (1 - 2/p^2 + 1/p^3) + Product_{p prime} (1 - 3/p^2 + 2/p^3) = A059956 - 2 * A065464 + A065473.

%F Equals A229099^2 * A394712.

%e 0.038175518934316482333638076884557187617887465418664...

%o (PARI) 6/Pi^2 - 2 * prodeulerrat(1 - 2/p^2 + 1/p^3) + prodeulerrat(1 - 3/p^2 + 2/p^3)

%Y Cf. A013929, A059956, A065464, A065473, A229099, A394712.

%K nonn,cons

%O 0,2

%A _Amiram Eldar_, Mar 30 2026