Amicable Numbers

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amicable numbers [′am·ə·kə·bəl ′nəm·bərz]

(mathematics)

Two numbers such that the exact divisors of each number (except the number itself) add up to the other number.

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.

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No references found			Well-represented here are Euler's contributions to geometry, including his enhancements of Pythagoras, number theory, including his work on odd perfect numbers and amicable numbers, combinatorics, including his work on Venn diagrams and orthogonal matrices, and a full range of his work in analysis, one article of which shows how Euler discovered America. How Euler did it by SciTech Book News			ametropia Amfiteatrov, Aleksandr Amfiteatrov, Aleksandr Valentinovich Amfortas Amga Amga Layer Amgot Amguema Amgun Amhara Amharic Amharic language Amherst Amherst College Amherst County Amherst, Jeffery Amherst, 1st Baron Amherst, Jeffery Amherst, Baron Amherstburg Amherstburg Heritage Homecoming amherstite Ami AMI BIOS Ami du Peuple AMI2 amianthus Amicable Numbers Amicalola Falls State Park & Lodge Amici prism Amici, Giovanni Battista amicron amictic amictic lake amicus curiae Amida Amidas, Philip amidase amidation amide amide hydrolysis amidine Amidism amido amidohydrolase amidol Amidopyrine Amidostomosis amidourea hydrochloride amidships Amiel, Henri Frédéric Amiens Amiens Charter			Amianthus lapis Amiantit Fiberglass Industries Ltd. Amiantit Rubber Industries, Ltd. amiantus amiantus AMIAP AMIAQ Amias Amias AMIAT AMIAV AMIB AMIBA AMIBIOS AMIC AMIC Amic acid Amic Young Communicators Network Amica AMICAALL AMICAAR amicability amicability amicable amicable Amicable action Amicable action Amicable number Amicable number Amicable number Amicable Numbers amicableness amicableness amicably amicably AMICAL Amical protection Amical protection Amical protection Amical protectorate Amical protectorate Amical protectorate Amical Vélo Club Nîmois Amicale Alpine Renault du Cher Amicale Anglo Cabrio Rennais Amicale Athoise des Amateurs d'Automobiles Anciennes Amicale Azuréenne des Amateurs d'Alpine Amicale Belge des Clubs Citroën Amicale Berline Coupé Cabriolet Fiat Amicale Bouliste de Clairfayts Amicale Cheminote des Coureurs de Fond Amicale Citroën Internationale Amicale de Dion Bouton Amicale de la Jeunesse de Montmoreau Amicale de La Vallée de La Vauvre Amicale de Moto et Scooter Anciens Amicale de Véhicules de Collection du Centre Amicale des Amateurs d'Automobiles Anciennes Amicale des Amateurs de Véhicules Anciens Amicale des Anciens des Services Spéciaux de la Défense Nationale Amicale des Anciens Volontaires-Francais en Espagne Republicaine

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