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Amicable numbers

Number theory

A pair of distinct positive integers, each equal to the sum of the other’s proper divisors. The smallest pair is 220 and 284.

What is usually left out

Distinctness is not decoration. Without it, every perfect number would pair with itself and the definition would swallow the previous entry. Whether infinitely many amicable pairs exist is open, as is whether any pair consists of one even and one odd number.

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