I want to find out the number of integers whose biggest non-trivial divisor is exactly $k$ times the smallest non-trivial divisor of that integer.
My thoughts are, that the smallest divisor $n$ has to be prime, otherwise the divisor would have smaller divisors, which would divide the larger integer too. Also the biggest divisor would be $kn$. Also I believe that the integers have to be in the form $mkn$, and then I would have to exclude some of these integers because the property does not hold, but i am not sure how to prove that.