amicable numbersAmicableNumbers2006-04-27 16:18:002006-04-28 09:30:00Definition% this is the default PlanetMath preamble. as your knowledge
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\newcommand{\Cl}{\operatorname{Cl}}\begin{defn}
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.
\end{defn}
\begin{exa}
The smallest amicable pair is $n=220$ and $m=284$. Indeed the sum of proper divisors of $220$ is:
$$1+2+4+5+10+11+20+22+44+55+110=284$$
and the sum of proper divisors of $284$ is:
$$1+2+4+71+142=220.$$
\end{exa}