What is "amicable numbers"

Amicable \Am"i*ca*ble\, a. [L. amicabilis, fr. amicus friend, fr. amare to love. See Amiable.] Friendly; proceeding from, or exhibiting, friendliness; after the manner of friends; peaceable; as, an amicable disposition, or arrangement.

That which was most remarkable in this contest was . . . the amicable manner in which it was managed.
--Prideoux.

Amicable action (Law.), an action commenced and prosecuted by amicable consent of the parties, for the purpose of obtaining a decision of the court on some matter of law involved in it.
--Bouvier.
--Burrill.

Amicable numbers (Math.), two numbers, each of which is equal to the sum of all the aliquot parts of the other.

Syn: Friendly; peaceable; kind; harmonious.

Usage: Amicable, Friendly. Neither of these words denotes any great warmth of affection, since friendly has by no means the same strength as its noun friendship. It does, however, imply something of real cordiality; while amicable supposes very little more than that the parties referred to are not disposed to quarrel. Hence, we speak of amicable relations between two countries, an amicable adjustment of difficulties. ``Those who entertain friendly feelings toward each other can live amicably together.''

n. (amicable number English)

Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number. (A proper divisor of a number is a positive factor of that number other than the number itself. For example, the proper divisors of 6 are 1, 2, and 3.) 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.

The smallest pair of amicable numbers is ( 220, 284). They are amicable because the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220.

The first ten amicable pairs are: (220, 284), (1184, 1210), (2620, 2924), (5020, 5564), (6232, 6368), (10744, 10856), (12285, 14595), (17296, 18416), (63020, 76084), and (66928, 66992).. (Also see and )