Problem:
For the positive integer , let denote the sum of all the positive divisors of with the exception of itself. For example, and . What is
Answer Choices:
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E.
Solution:
The positive divisors of , other than , are , and , so . As a consequence, we also have .
Note: A positive integer whose divisors other than itself add up to that positive integer is called a perfect number. The two smallest perfect numbers are and .
The problems on this page are the property of the MAA's American Mathematics Competitions