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Amicable Numbers

Find a number's amicable partner and list every amicable pair up to a limit.

In number theory, two different numbers form an amicable pair when each one equals the sum of the other's proper divisors. The proper divisors of a number are all of its positive divisors except the number itself.

Example: the proper divisors of 220 sum to 284, and the proper divisors of 284 sum to 220, so 220 and 284 are an amicable pair.

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