OMM 2019 Problem 1

An integer number $m\geq 1$ is mexica if it's of the form $n^{d(n)}$ , where $n$ is a positive integer and $d(n)$ is the number of positive integers which divide $n$ . Find all mexica numbers less than $2019$ .

Note. The divisors of $n$ include $1$ and $n$ ; for example, $d(12)=6$ , since $1, 2, 3, 4, 6, 12$ are all the positive divisors of $12$ .

Proposed by Cuauhtémoc Gómez