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amicable numbers (Definition)
Definition 1   Two natural numbers $ n$ and $ m$ are amicable numbers (an amicable pair or simply amicable) if each is the sum of the proper divisors of the other.
Example 1   The smallest amicable pair is $ n=220$ and $ m=284$. Indeed the sum of proper divisors of $ 220$ is:
$\displaystyle 1+2+4+5+10+11+20+22+44+55+110=284$
and the sum of proper divisors of $ 284$ is:
$\displaystyle 1+2+4+71+142=220.$



"amicable numbers" is owned by alozano.
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See Also: abundant number, deficient number

Other names:  amicable pair, amicable

Attachments:
a formula for amicable pairs (Definition) by alozano
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Cross-references: proper divisors, sum, natural numbers
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This is version 3 of amicable numbers, born on 2006-04-27, modified 2006-04-28.
Object id is 7875, canonical name is AmicableNumbers.
Accessed 3208 times total.

Classification:
AMS MSC: 11A05 (Number theory :: Elementary number theory :: Multiplicative structure; Euclidean algorithm; greatest common divisors)
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