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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.

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