Can anyone help me with this?
Consider a positive natural number of the form $n=p_1^{a_1}\dots p_m^{a_m}$ where $p_1,\dots ,p_m$ are unique prime numbers and $a_1, \dots ,a_m \in \mathbb{N}$
a) How many unique divisors does $n$ have of the form $(x·y·z)$, where $x, y, z$ are unique prime numbers?
b) How many ways are there to create an ordered list of all of the unique positive divisors of $n$?
For a) I just know that it uses combinations, then the number of unique divisors is given by $C(m,3)$.
For b) I found out that there are $a_i+1$ choices for some $i$. Hence $(a_1+1)(a_2+1)\dots (a_m+1)$ number of unique positive divisors.
Thanks for any insights.