Question 153
For a positive integer $n$, let $f(n)$ be the number of divisors of $n$ which are perfect squares, and let $g(n)$ be the number of divisors of $n$ which are perfect cubes. Determine whether there exists an integer $n$ such that
$$
\frac{f(n)}{g(n)}=2012
$$
$$
\frac{f(n)}{g(n)}=2012
$$