 Buchstab theorem

For each fixed $u>1$, the number $\Phi (z^u,z)$ of z-sieved numbers at most $z^u$ satisfies $\Phi (z^u,z)\sim z^{u}w(u)/\log z$ as $z\to \infty$. The fixed-$u$ asymptotic does not extend to $u=1$.