Euler Project: Problem 12

The sequence of triangle numbers is generated by adding the natural numbers. So the 7^th 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?

import Data.Numbers.Primes -- Must primes-0.2.1.0
import Data.List
import Data.Maybe 

main :: IO()
main = print $ head $ mapMaybe (tellAbove 500) $ zipFn tagNo 

tagNo :: [Int]
tagNo = [sum [1..n] | n <- [1..]] 

tellAbove :: Int -> (Int, Int) -> Maybe Int
tellAbove x (a, b)
| b >= x = Just a
| otherwise = Nothing 

zipFn :: [Int] -> [(Int, Int)]
zipFn xs = zip xs (facLength xs) 

facLength :: [Int] -> [Int]
facLength = map (length . getFactors) 

getFactors :: Int -> [Int]
getFactors x = map product . nub . subsequences $ primeFactors x

*Main> main
76576500