# Non-trivial divisors

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.

• Note that every number (with at least 1 non-trivial divisor) is the product of their smallest and largest non-trivial divisors. This means your number is $kn^2$ for $n$ prime and $k$ having no prime factors less than $n$. – Don Thousand Apr 2 at 0:46
• so the smallest non-trivial divisor has to be prime, and then I get the integer $kn^2$, but the relationship to the number of such integers still eludes me – M-S-R Apr 2 at 0:59