# 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 ...

### A dictionary of science, literature and art, ed. by W.T. Brande assisted by J. Cauvin. ed. by W.T. Brande and G.W. Cox.3 vols (1865)

by Dictionary

**Amicable Numbers**. Two numbers are gaud to be amicable when each is equal
to the sum of the aliquot parts of the other. The first or least pair of amicable
numbers are 220 and 284 ; they were found by E.Schooten, with whom the name
...

### A Dictionary of Science, Literature, & Art (1875)

Comprising the Definitions and Derivations of the Scientific Terms in General Use, Together with the History and Descriptions of the Scientific Principles of Nearly Every Branch of Human Knowledge by William Thomas Brande, George William Cox

**Amicable Numbers**. Two numbers are said to be amicable when each is equal to
the sum of the aliquot parts of the other. The first or least pair of amicable
numbers are 220 and 284; they were found by E.Schooten, with whom the name
...

### CHAMBERS'S ENCYCLOPAEDIA: A DICTIONARY OF UNIVERSAL KNOWLEDGE FOR THE PEOPLE (1878)

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

### The Encyclopaedia Britannica (1911)

A Dictionary of Arts, Sciences, Literature and General Information by Hugh Chrisholm

**Amicable numbers** were known to the Pythagoreans, who accredited them with
many mystical properties. A general formula by which these numbers could be
derived~ was invented by the Arabian astronomer Tobit ben Korra (836-901): if ...

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