Question

The 5-digit number, $16807=7^5$, is also a fifth power. Similarly, the 9-digit number, $134217728=8^9$, is a ninth power.

How many n-digit positive integers exist which are also an nth power?

Haskell

main ::  IO ()
main = print $ sum $ [1 | i <- [1..99], n <- [1..99], length (show (i^n)) == n]

$ ghc -O2 -o nPower nPower.hs
$ time ./nPower
real   0m0.021s
user   0m0.021s
sys    0m0.000s

Python

#!/usr/bin/env python
print(sum(1 for i in range(1,100) for x in range(1,100) if len(str(i**x)) == x))

$ time python3 n-power.py
real   0m0.028s
user   0m0.028s
sys    0m0.000s