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An integer n is said to be y-friable if its largest prime factor $P^+(n)$ isless than y. In this paper, it is shown that the y-friable integers less than xhave a weak exponent of distribution at least $3/5-\varepsilon$ when $(\logx)^c\leq y\leq x^{1/c}$ for some $c=c(\varepsilon)\geq 1$, that is, they arewell distributed in the residue classes of a fixed integer $a$, on average overmoduli $\leq x^{3/5-\varepsilon}$ 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 onprevious work of Fouvry and Tenenbaum. Our proof combines the dispersion methodof Linnik in the setting of Bombieri, Fouvry, Friedlander and Iwaniec, andrecent work of Harper on friable integers in arithmetic progressions.

Th\'eor\`emes de type Fouvry--Iwaniec pour les entiers friables