# [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<sub>1</sub><sup>α<sub>1</sub></sup>⋯p<sub>m</sub><sup>α<sub>m</sub></sup>**, where **α<sub>m</sub> > 0**.

We have that **a<sup>b</sup>** (**b>1**) for some positive integer **a** if and only if **b** is a divisor of all exponents **α<sub>j</sub>**. 

Thus, an integer **k > 1** is a perfect power if and only if **gcd(α<sub>1</sub>, ⋯, α<sub>m</sub>) ≠ 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 > 0 and 1 otherwise.
                 This maps 1 -> [0] and [0] -> [1].
         g/      Reduce the list of exponents by GCD.
                 In particular, we achieved that 1 -> 0 and 0 -> 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.

[bytes]: https://github.com/DennisMitchell/jelly/wiki/Code-page
[Jelly]: http://github.com/DennisMitchell/jelly
[Try it online!]: http://jelly.tryitonline.net/#code=wrXDhkU7wqxnL-KAmcK1I-G5qg&input=MTA