** Amicable numbers** are two different

*numbers*so related that the sum of the proper divisors of each is equal to the other

*number.*

See “proper divisor”

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

They are

amicablebecause 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 next **amicable number** is (1184, 1210). Therefore there is only one **amicable number** from 0 to 1000.

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