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
Problem
Source: Mexico National Olympiad 2019 Problem 1
Tags: number theory, number of divisors, Perfect power, function