Let $a,q$ be co-prime integers and let $P(a,q)$ denote the set of primes congruent to $a$ modulo $q$. Is it known whether one can give an asymptotic formula for the expression

$$\displaystyle \sum_{\substack{n \leq x \\ p | n \Rightarrow p \in P(a,q)}} d(n),$$ where $d(n)$ is the number of divisors of $n$?