# Amicable numbers

On this page:

## 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

Click on a title to look inside that book (if available):

### A Philosophical and Mathematical Dictionary (1815)

Containing an Explanation of the Terms, and an Account of the Several Subjects, Comprised Under the Heads Mathemetics, Astronomy, and Philosophy Both Natural and Experimental; with an Historical Account of the Rise, Progress and Present State of These Sciences; Also Memoirs of the Lives and Writings of the Most Eminent Authors, Both Ancient and Modern, who by Their Discoveries Or Improvements Have Contributed to the Advancement of Them by Charles Hutton

**AMICABLE numbers**, denote pairs
of numbers, of which each of them is mutually equal to the sum of all the aliquot
parts of the ...

### Mathematical Dictionary and Cyclopedia of Mathematical Science Comprising Definitions of All the Terms Employed in Mathematics - (1859)

An Analysis of Each Branch, and of the Whole, as Forming a Single Science

Thus, 220 and 234, arc **amicable numbers** The aliquot parts of the first are
0, 2, ...

## Online dictionaries and encyclopedias with entries for Amicable numbers

Click on a label to prioritize search results according to that topic:

## Share this page

## Next...

Go to the pronunciation of Amicable numbers to learn how to say it correctly!