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| Title of object: |
amicable numbers |
| Canonical Name: |
AmicableNumbers |
| Type: |
Definition |
| Created on: |
2006-04-27 16:18:00 |
| Modified on: |
2006-04-27 16:29:23 |
| Classification: |
msc:11A05 |
| Synonyms: |
amicable numbers=amicable pair
amicable numbers=amicable |
Revision comment (for changes between this and next version):
| Changes for correction #7879 ('typo'). |
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Content:
\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 $n=284$. 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} |
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