Amicable Numbers

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amicable numbers

[′am·ə·kə·bəl ′nəm·bərz]
Two numbers such that the exact divisors of each number (except the number itself) add up to the other number.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Amicable Numbers


a pair of natural numbers, each of which is equal to the sum of all the exact divisors of the other, that is, divisors that are different from the number itself. The amicable numbers 284 and 220, whose corresponding sums of divisors are 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284 and 1 + 2 + 4 + 71 + 142 = 220, were already known in antiquity. Assigning a mystical meaning to the properties of numbers, the Pythagoreans attached great importance to amicable numbers. L. Euler found approximately 60 pairs of amicable numbers. The use of computers has made it possible to find several hundred more pairs of amicable numbers. These numbers are primarily of historical interest.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.