Find the n-th perfect power! A perfect power is a number of the form \$a^b\$, where \$a&gt;0\$ and \$b&gt;1\$.
For example, \$125\$ is a perfect power because it can be expressed as \$5^3\$.
Goal
Your task is to write  a program/function that finds the \$n\$-th perfect power, given a positive integer \$n\$.
Specs

The first perfect power is \$1\$ (which is \$1^2\$).
Input/output in any reasonable format.
Built-ins are allowed.

Further information

OEIS A001597

Scoring
This is code-golf. Shortest solution in bytes wins.
Testcases
input  output
1      1
2      4
3      8
4      9
5      16
6      25
7      27
8      32
9      36
10     49
Jelly, 11 bytes
µÆE;¬g/’µ#Ṫ

Try it online!.
Background
Every positive integer \$k\$ can be factorized uniquely as the product of powers of the first \$m\$ primes, i.e., \$k=p_1^{\alpha_1}\cdots p_m^{\alpha_m}\$, where \$\alpha_m&gt;0\$.
We have that \$a^b\$ (\$b&gt;1\$) for some positive integer \$a\$ if and only if \$b\$ is a divisor of all exponents \$\alpha_j\$.
Thus, an integer \$k &gt; 1\$ is a perfect power if and only if \$\gcd(α_1, ⋯, α_m) ≠ 1\$.
How it works
µÆE;¬g/’µ#Ṫ  Main link. No arguments.

µ            Make the chain monadic, setting the left argument to 0.
        µ#   Find the first n integers k, greater or equal to 0, for which the
             preceding chain returns a truthy value.
             In the absence of CLAs, n is read implicitly from STDIN.
 ÆE          Compute the exponents of the prime factorization of k.
   ;¬        Append the logical NOT of k, i.e., 0 if k &gt; 0 and 1 otherwise.
             This maps 1 -&gt; [0] and [0] -&gt; [1].
     g/      Reduce the list of exponents by GCD.
             In particular, we achieved that 1 -&gt; 0 and 0 -&gt; 1.
       ’     Decrement; subtract 1 from the GCD.
             This maps 1 to 0 (falsy) and all other integers to a truthy value.
          Ṫ  Tail; extract the last k.