-- https://projecteuler.net/problem=29
-- Consider all integer combinations of a^b for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

-- 22=4, 23=8, 24=16, 25=32
-- 32=9, 33=27, 34=81, 35=243
-- 42=16, 43=64, 44=256, 45=1024
-- 52=25, 53=125, 54=625, 55=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?

import Data.Set
import qualified Data.Set as Set
import Data.List

cartProd xs ys = [x^y | x <- xs, y <- ys]

countPowers n = size (fromList (cartProd [2..n] [2..n]))
countPowers2 n = length (nub [x^y | x <- [2..n], y <- [2..n]])