Euler12.hs

import Data.List

primes :: [Int]
primes = 2 : 3 : 5 : filter isPrime [7, 9 ..]
              
suspects :: Int -> [Int]
suspects n = takeWhile (\x -> x * x <= n) primes
         
isPrime :: Int -> Bool
isPrime n = all (\x -> n `mod` x /= 0) (suspects n) 

factorize :: Int -> [(Int, Int)]
factorize n = f [x | x <- suspects n, n `mod` x == 0] where
  f []     = [(n, 1)]
  f (x:xs) = (x, r) : factorize m where
    (r, m) = n `factorBy` x
      
factorBy :: Int -> Int -> (Int, Int) 
factorBy a b = fp 0 a where
  fp x a | r == 0    = fp (x + 1) q
         | otherwise = (x, a)
    where (q, r) = a `divMod` b 

divisors :: Int -> Int
divisors n = product [x + 1 | (_, x) <- factorize n]

triangles :: [Int]
triangles = scanl1 (+) [1..]

answer = find ok triangles where
  ok x = divisors x > 500