Improve code in a few Haskell solutions

Haskell/ProjectEuler.hs

@@ -23,7 +23,7 @@ digitSum n = sum $ map digitToInt $ show n
 
 
 sumProperDivisors :: (Integral a) => a -> a
-sumProperDivisors n = sum [ if x /= y then x + y  else x | x <- [2..ceiling $ sqrt $ fromIntegral n], let y = n `div` x, n `mod` x == 0 ] + 1
+sumProperDivisors n = sum [ if x /= y then x + y  else x | x <- [2..floor $ sqrt $ fromIntegral n], let y = n `div` x, n `mod` x == 0 ] + 1
 
 
 countDivisors :: (Integral a) => a -> Int

Haskell/p001.hs

@@ -3,7 +3,7 @@
 -- Find the sum of all the multiples of 3 or 5 below 1000.
 
 sumMultiples :: Integer
-sumMultiples = sum(filter p [ n | n <- [1..999] ])
+sumMultiples = sum $ filter p [ n | n <- [1..999] ]
                 where p n = n `mod` 3 == 0 || n `mod` 5 == 0
 
 main =  do

Haskell/p003.hs

@@ -5,9 +5,9 @@ import ProjectEuler (isPrime)
 
 maxPrimeFactor :: Integer -> Integer
 maxPrimeFactor n
-    | isPrime n         = n         
-    | n `mod` 2 == 0    = maxPrimeFactor $ n `div` 2
-    | otherwise         = maxPrimeFactor $ n `div` head [i | i <- [3,5..], n `mod` i == 0 && isPrime i]
+    | isPrime n = n         
+    | even n    = maxPrimeFactor $ n `div` 2
+    | otherwise = maxPrimeFactor $ n `div` head [i | i <- [3,5..], n `mod` i == 0 && isPrime i]
 
 main = do
     let result = maxPrimeFactor 600851475143

Haskell/p006.hs

@@ -10,7 +10,7 @@
 --
 --Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
 
-sumSquareDiff :: Integer -> Integer
+sumSquareDiff :: (Integral a) => a -> a
 sumSquareDiff n = (sum [1..n]^2) - (sum $ map (^2) [1..n])
 
 main = do

Haskell/p009.hs

@@ -9,7 +9,7 @@
 -- Find the product abc.
 
 pythagoreanTriplet :: (Integral a) => a -> (a, a, a)
-pythagoreanTriplet n = head [ (x, y, z) | x <- [1..n], y <- [1..n], z <- [1..n], x + y + z == n, x^2 + y^2 == z^2]
+pythagoreanTriplet n = head [ (x, y, z) | x <- [1..n], y <- [x..n], z <- [y..n], x + y + z == n, x^2 + y^2 == z^2]
 
 prodTriplet :: (Integral a) => (a, a, a) -> a
 prodTriplet (x, y, z) = x * y * z

Haskell/p016.hs

@@ -6,5 +6,5 @@ import ProjectEuler (digitSum)
 
 main = do
     let result = digitSum $ 2 ^ 1000
-    putStrLn $ "Project Euler, Problem 10\n"
+    putStrLn $ "Project Euler, Problem 16\n"
         ++ "Answer: " ++ (show result)