Euler_12.hs

module Euler12 (triangle,multipleCount) where
import Data.List

triangle :: Int -> Int 
triangle n = head . dropWhile (\m -> multipleCount m < n) $ [ i*(i+1) `div` 2 | i <- [1..] ]

multipleCount :: Int -> Int
multipleCount number = 
        product $ map (+1) $ map length (group pFactors)
        where pFactors = primeFactors [] number 2

primeFactors :: [Int] -> Int -> Int -> [Int]
primeFactors acc n m
        | (isPrime n) = n:acc
        | (rmd == 0) = primeFactors acc' n' m
        | otherwise = primeFactors acc n (nextPrime m)
        where   rmd = n `mod` m
                n' = n `div` m
                acc' = m:acc

nextPrime :: Int -> Int
nextPrime 2 = 3
nextPrime n = head $ dropWhile (not . isPrime) [n+2,n+4..]

isPrime :: Int -> Bool
isPrime 2 = True
isPrime number = (number `mod` 2 /= 0)
              && (null range || not (any (\divisor -> number `mod` divisor == 0) range))
        where   upper = 1+truncate(sqrt(fromIntegral(number)))
                range = [3,5..upper]