Solving a Word Problem relating to factorisation [closed]

The $\text{Ionof}$ (Integer on number of factors) of an integer is the integer divided by the number of factors it has. For example, $18$ has $6$ factors so $\text{Ionof}(18) = \frac{18}{6} = 3$, and $27$ has $4$ factors so $\text{Ionof}(27) = \frac{27}{4} = 6.75$.

a) Find $\text{Ionof}(36)$

b) Explain why $\text{Ionof}(pq)$ is not an integer if $p$ and $q$ are distinct primes.

c) If $p$ and $q$ are distinct primes, find all numbers of the form $(pq)^4$ whose $\text{Ionof}$ is an integer.

d) Show that the square of any prime number is the $\text{Ionof}$ of some integer.

Okay. I'll leave the problem a) for you.

For the second one. Observe the $pq$ has 4 distinct factors, namely $(1, p, q, pq)$. Also, observe that $p$ and $q$ are distinct prime i.e. that both of them can't be $2$. So, since all other prime numbers are odd, $pq$ isn't a multiple of $4$ which is the number of prime factors. Hence, $\text{Ionof}(pq)$ isn't an integer.