# Amicable numbers

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## Explanation

**Amicable numbers** are two different numbers so related that the sum of the proper divisors of each is equal to the other number. A pair of amicable numbers constitutes an aliquot sequence of period 2. A related concept is that of a perfect number, which is a number that equals the sum of its own proper divisors, in other words a number which forms an aliquot sequence of period 1. Numbers that are members of an aliquot sequence with period greater than 2 are known as sociable numbers.

- also known as Amicable number

## Printed dictionaries and other books with definitions for Amicable numbers

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### United Editors Encyclopedia and Dictionary (1907)

A Library of Universal Knowledge and an Unabridged Dictionary of the English Language ...

**Amicable numbers** are pairs of numbers, either
one of ...

### Historical Encyclopedia of Natural and Mathematical Sciences (2009)

by Ari Ben-Menahem

**Amicable numbers** intrigued the Greeks, Arabs and many other
since antiquity193. The mathematician Thabit Ibn Qurra al-Harrani (ca 855 CE) ...

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