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 0m0.000sPython
#!/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