Number of squarefree numbers with three distinct prime factors below $N$

Is there any way to calculate the number of squarefree numbers with three distinct prime factors below given $N$? I.e. how many numbers below $N$ can be factored to the form $$prq$$ where $p$,$r$ and $q$ are distinct prime numbers?

Thanks!

The number of possibilities will depend on the primes less than $N$. Taking the primes to be in ascending size $p<r<q$, we can see that $p<\sqrt[3]N, r<\sqrt{N/2}$ and $q<N/6$. Of course the restriction that the product is less than $N$ will also reduce the options significantly - for example, for $p=5$ and $r=13$, $q$ has a much lower maximum, $N/65$.