021-amicable-numbers.lhs

#!/usr/bin/env runhaskell

[Amicable numbers](http://projecteuler.net/problem=21)

Let d(n) be defined as the sum of proper divisors of n (numbers less than n
which divide evenly into n).
If d(a) = b and d(b) = a, where a  b, then a and b are an amicable pair and each
of a and b are called amicable numbers.

For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55
and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and
142; so d(284) = 220.

Evaluate the sum of all the amicable numbers under 10000.


Code
----

> import Divisors

> main :: IO ()
> main = let result = sum
>                   $ filter amicable [1 .. 10000]
>        in print result


Answer
------

    31626