012-highly-divisible-triangular-number.lhs

#!/usr/bin/env runhaskell

[Highly divisible triangular number](http://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?


Code
----

> import Divisors

> triangularNumbers :: [Integer]
> triangularNumbers = scanl1 (+) [1..]

> numDivisors :: Integer -> Int
> numDivisors = length . divisors

> main :: IO ()
> main = let res = head
>                $ filter (\ n -> numDivisors n > 500) triangularNumbers
>        in print res


Answer
------

    76576500


Performance
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    41.74s user 0.20s system 100% cpu 41.865 total