n-factorful.hs

keepDiv :: Int -> Int -> Int
keepDiv x n
    | x `mod` n == 0 = keepDiv (x `div` n) n
    | otherwise      = x

nfacts' :: Int -> Int -> Int
nfacts' 1 _ = 0
nfacts' x n
    | x `mod` n == 0 = 1 + nfacts' (x `keepDiv` n) (n + 1)
    | otherwise      = nfacts' x (n + 1)

nfacts :: Int -> Int
nfacts x = nfacts' x 2

solve :: [Int] -> Int
solve [a,b,n] = length $ filter (\x -> nfacts x == n) [a..b]

input :: [String] -> String
input [] = ""
input x = show $ solve $ map readInt x

readInt :: String -> Int
readInt x = read x :: Int

main = do interact $ unlines . map (input . words) . tail . lines