# Project Euler

## Amicable numbers

### 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.

This problem can modify the function built for problem 12 to find a divisor of a number to return the sum of the divisors of a number. Notice this divisor sum function should only check up to the because any divisor found below the will have a corresponding divisor above and simply obtained by dividing the first divisor found into the number the divisor came from. Of course, a perfect square need to count the value only once. Once a divisor sum function is presented, to check , an array is setup to remember which number has a corresponding amicable numbers to add these number up at the end and eliminate the need to recalculate any i.