2008 AMC 10A Problems/Problem 3

Problem

For the positive integer $n$ , let $\langle n\rangle$ denote the sum of all the positive divisors of $n$ with the exception of $n$ itself. For example, $\langle 4\rangle=1+2=3$ and $\langle 12 \rangle =1+2+3+4+6=16$ . What is $\langle\langle\langle 6\rangle\rangle\rangle$ ?

$\mathrm{(A)}\ 6\qquad\mathrm{(B)}\ 12\qquad\mathrm{(C)}\ 24\qquad\mathrm{(D)}\ 32\qquad\mathrm{(E)}\ 36$

Solution

$<<<6>>>\ =\ <<6>>\ =\ <6>\ =\ 6\quad\Longrightarrow\quad\mathrm{(A)}$

2008 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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All AMC 10 Problems and Solutions

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2008 AMC 10A Problems/Problem 3

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