test.hs

factors1 :: Integer -> Integer -> [Integer]
factors1 k n
    | k * k > n = [n]
    | n `mod` k == 0 = k : factors1 k (n `div` k)
    | otherwise = factors1 (k + 1) n

factors :: Integer -> [Integer]
factors 1 = []
factors n = factors1 2 n

hasRepeat :: [Integer] -> Bool
hasRepeat [] = False
hasRepeat [_] = False
hasRepeat (x : y : xs) = x == y || hasRepeat (y : xs)

squareFreeFrom :: Integer -> [Integer]
squareFreeFrom n =
    let rest = squareFreeFrom (n + 1)
    in if hasRepeat (factors n) then rest else n : rest
                             
squareFree :: [Integer]
squareFree = squareFreeFrom 1

root :: Integer -> Integer -> Integer -> Integer
root lo hi n =
    if hi < lo then hi
    else let mid = (lo + hi) `div` 2
         in if mid * mid <= n then root (mid + 1) hi n
                              else root lo (mid - 1) n

squareRoot :: Integer -> Integer
squareRoot n = root 1 n n