-- Highly divisible triangular number

-- 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?


main = do
    print (trial_division 2 10)
    print (find_triangular 1)


find_triangular :: Int -> Int
find_triangular n
    | trial_division 2 nth_triangular > 100 = nth_triangular
    | otherwise = find_triangular (n + 1)
    where nth_triangular = (n * (n + 1)) `div` 2

trial_division :: Int -> Int -> Int
trial_division by x
    | x == 0 || by > x = 2
    | x `mod` by == 0 = 1 + trial_division by (x `div` by)
    | otherwise = trial_division (by + 1) x

-- naive
-- triangulars :: Int -> [Int]
-- triangulars 0 = []
-- triangulars i = sum [1..i] : triangulars (i - 1)