Buchstab theorem
= Buchstab theorem
{c}
= Buchstab's theorem
{c}
{synonym}
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 $u=1$.