Amicable numbers

Amicable numbers are two different numbers so related that the sum of the proper divisors of one of the numbers is equal to the other. (A proper divisor of a number is a positive integer divisor other than the number itself. For example, the proper divisors of 6 are 1, 2, and 3.) A pair of amicable numbers constitutes an aliquot sequence of period 2. A related concept is that of a perfect number, which is a number which equals the sum of its own proper divisors, in other words a number which forms an aliquot sequence of period 1.

For example, the smallest pair of amicable numbers is (220, 284); for the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71, and 142, of which the sum is 220.

The first few amicable pairs are: (220, 284), (1184, 1210), (2620, 2924), (5020, 5564), (6232, 636