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-- 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)
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