  An integer n is said to be y-friable if its largest prime factor $P^+(n)$ is
less than y. In this paper, it is shown that the y-friable integers less than x
have a weak exponent of distribution at least $3/5-\varepsilon$ when $(\log
x)^c\leq y\leq x^{1/c}$ for some $c=c(\varepsilon)\geq 1$, that is, they are
well distributed in the residue classes of a fixed integer $a$, on average over
moduli $\leq x^{3/5-\varepsilon}$ for each fixed $a\neq 0$ and $\varepsilon>0$.
We present an application to the estimation of the sum $\sum_{2\leq n\leq x,
P^+(n)\leq y}\tau(n-1)$ when $(\log x)^c\leq y$. This follows and improves on
previous work of Fouvry and Tenenbaum. Our proof combines the dispersion method
of Linnik in the setting of Bombieri, Fouvry, Friedlander and Iwaniec, and
recent work of Harper on friable integers in arithmetic progressions.
