# Amicable Numbers

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**Amicable numbers **are two different numbers so related that the sum of the proper divisors of each is equal to the other number.

The smallest pair of amicable numbers is (220, 284).

They are amicable because 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.

Write an algorithm that will find and print out all the Amicable number sets that are less than 1000