Divisors

Number Theory Level 2

$\begin{array} { | c | c | } \hline \text{Number} & \text{ Number of positive divisors} \\ \hline 1 & 1 \\ 2\times2 & 3 \\ 3\times3\times3 & 4 \\ 4\times4\times4\times4 & 9 \\ \hline \end{array}$

True or False?

As $n$ increases, the number of positive divisors of $\underbrace{n\times n\times \cdots \times n}_{n\text{ times}}$ increases.