-- Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
--
-- 2^2=4, 2^3=8, 2^4=16, 2^5=32
-- 3^2=9, 3^3=27, 3^4=81, 3^5=243
-- 4^2=16, 4^3=64, 4^4=256, 4^5=1024
-- 5^2=25, 5^3=125, 5^4=625, 5^5=3125
--
-- If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:
--
-- 4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
--
-- How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

module P029 (p029) where

import Data.List (nub)

powerCombinations :: (Integral a) => a -> [a]
powerCombinations n = nub [x ^ y | x <- [2 .. n], y <- [2 .. n]]

p029 :: IO ()
p029 = do
  let result = length $ powerCombinations 100
  putStrLn $
    "Project Euler, Problem 29\n"
      ++ "Answer: "
      ++ show result