Project Euler, Problem #12, Haskell

-- The sequence of triangle numbers is generated by adding the natural
-- numbers. So the 7th triangle number would be
-- 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be: 1, 3,
-- 6, 10, 15, 21, 28, 36, 45, 55, ... Let us list the factors of the
-- first seven triangle numbers: 1: 1; 3: 1, 3; 6: 1, 2, 3, 6; 10: 1,
-- 2, 5, 10; 15: 1, 3, 5, 15; 21: 1, 3, 7, 21; 28: 1, 2, 4, 7, 14, 28
-- We can see that 28 is the first triangle number to have over five
-- divisors. What is the value of the first triangle number to have
-- over five hundred divisors?

-- Generate the infinite list of triangle numbers.
tn :: [Integer]
tn = scanl1 (+) [1 ..]

-- Take a number and return a tuple with the number and the number of
-- its divisors.
nad :: Integral c => c -> (c, Int)
nad n = (n, d * 2 - sna)
  where
    d
      | mod n 2 == 0 = length [q | q <- [1 .. srf n], mod n q == 0]
      | otherwise = length [q | q <- [1,3 .. srf n], mod n q == 0]
    srf = floor . sqrt . fromIntegral
    src = ceiling . sqrt . fromIntegral
    sna
      | srf n /= src n = 0
      | otherwise = 1

-- Check if the number of divisors is greater than five hundred.
ndgfh :: (Ord a, Num a) => (t, a) -> Bool
ndgfh (_, d)
  | d > 500 = True
  | otherwise = False

main :: IO ()
main = print $ fst $ head $ filter ndgfh $ map nad tn

-- 76576500

-- real 0m8,009s
-- user 0m7,966s
-- sys  0m0,032s