Divisors

Number Number of positive divisors112×233×3×344×4×4×49 \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 nn increases, the number of positive divisors of n×n××nn times\underbrace{n\times n\times \cdots \times n}_{n\text{ times}} increases.

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