  An integer is said to be $y$-friable if its greatest prime factor P(n) is
less than $y$. In this paper, we study numbers of the shape $n-1$ when
$P(n)\leq y$ and $n\leq x$. One expects that, statistically, their
multiplicative behaviour resembles that of all integers less than $x$.
Extending a result of Basquin, we estimate the mean value over shifted friable
numbers of certain arithmetic functions when $(\log x)^c \leq y$ for some
positive $c$, showing a change in behaviour according to whether $\log y /
\log\log x$ tends to infinity or not. In the same range in $(x, y)$, we prove
an Erd\"os-Kac-type theorem for shifted friable numbers, improving a result of
Fouvry and Tenenbaum. The results presented here are obtained using recent work
of Harper on the statistical distribution of friable numbers in arithmetic
progressions.
