Amicable numbers

Amicable numbers love each other so much. How much? Well, lets take a classic pair 284 and 220 and see just how friendly they are. Lets take all the proper divisors of 220 (that is to say, all its divisors that leave no remainder, including the number 1, and excluding the number itself) and add them all up:

1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284

Now, lets take 284 and do the same thing:

1 + 2 + 4 +71 + 142 = 220.

These are a pair of amicable numbers. Other pairs include (1184, 1210), (2620, 2924), and (5020, 5564). This type of number pair was discovered and studied by the Pythagoreans and has been the subject of much research through the centuries. Fermat, Descartes, Iranian Muhammad Baqir Yazdi, are among the many mathematicians who have delved into the world of amicable numbers.