Find an $n$ not a power of a prime such that $n$ has 51 positive divisors

Question

Find an $n$ not a power of a prime such that $n$ has 51 positive divisors.

I'm not sure where to even start with this question. Any help would be really appreciated.

Answer 1

$51=3\cdot17$, therefore you can choose any primes $[p,q]$ and calculate $n=(p^{3-1})\cdot(q^{17-1})$.

For example, the smallest such value is $n=3^{3-1}\cdot2^{17-1}=3^{2}\cdot2^{16}=9\cdot65536=589824$.