We estimate the number of integers
n
n
up to
x
x
in the arithmetic progression
a
(
mod
q
)
a(\bmod q)
with
n
n
free of prime factors exceeding
y
y
. For a wide range of the variables
x
,
y
,
q
x,y,q
, and
a
a
we show that this number is about
x
/
(
q
u
u
)
x/(q{u^u})
, where
u
=
log
x
/
log
y
u = \log x/\log y
.