AMC 10 2008a Problem 3

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