Abelian groups of order n. 
Is there a number $n$ such that there are exactly 1 million abelian groups of order $n$?

Can anyone please explain. I would yes because numbers are infinitive, and so any number n can be expressed as a direct product of cyclic groups of order n.
Can anyone please help  me understand. 
Thank you.

If $n=\prod_{i=1}^rp_i^{k_i}$, then the number of distinct abelian groups of order $n$ is given by
$$
\prod_{i=1}^rp(k_i),
$$
where $p(k)$ denotes the number of partitions of $k$. Now $10^6=p(k_1)\cdots p(k_r)$ has to be solved. But $p(2)=2$ and $p(4)=5$, so we can solve it.
