Generalized Dirichlet theorem for primes in arithmetic sequences

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Dirichlet's theorem for arithmetic sequences of primes states that if $a$ and $b$ are coprime, then there exists an infinite number of prime numbers of the form $a+kb$.

My question is can we conclude, for similar $a$ and $b$ coprime and a fixed number $n$, there are an infinite number of numbers exactly the product of $n$ primes of the form $a+kb$?

(My question is motivated from thinking about this question.)