Amicable numbers are a pair of two distinct positive integers related so that the sum of the proper divisors of each number, meaning all its divisors other than itself, equals the other number exactly. The smallest and best known amicable pair, two hundred twenty and two hundred eighty-four, was already known to the Pythagoreans in ancient Greece, who regarded the pair as a symbol of friendship. The ninth century mathematician Thabit ibn Qurra found a general formula capable of generating some amicable pairs from certain prime numbers, and later mathematicians, including Pierre de Fermat, Rene Descartes and Leonhard Euler, found further pairs and extended Thabit's formula, with Euler alone identifying over fifty new amicable pairs. Amicable numbers are closely related to, but distinct from, perfect numbers, in which a single number's proper divisors sum to that same number rather than to a different partner number.
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1. Wikipedia: Amicable numbers
IntroductionQuote, Introduction
In mathematics, the amicable numbers are two different natural numbers related in such a way that the sum of the proper divisors of each is equal to the other number.
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