Euler 12

Euler12.hs

module Euler where

import Control.Monad
import Data.List
import Data.Numbers.Primes


{-

https://projecteuler.net/problem=12

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?
-}

-- FAST IMPLEMENTATION
-- http://xaviershay.github.io/project-euler/
-- the number of divisors a number has is equal to the product of the powers of each prime factor plus one
-- prime factors of 28 = 2^2 + 7^1 = (2+1) * (1+1) = 6
-- the divisors are 1,2,4,7,14,28

numDivisors :: Int -> Int
numDivisors 1 = 1
numDivisors n = foldl1 (*) . map ((+1) . length) . group . primeFactors $ n

triangleNumbers = scanl1 (+) [1..]
firstOver n = find ((>n) . numDivisors) triangleNumbers