We show Halasz's Theorem in intervals of length $x^{7/12}$ (removing integers with a prime factor larger than the length of the interval). The method extends to intervals of length $>x^{1/2+\epsilon}$ but restricting to $y$-smooth integers where $y$ is significantly smaller than the length of the interval.

In this article we study the similarities in the anatomies of integers and permutations.