2007 AMC 8 Problem 10

For any positive integer n, define \underline{\,n\,} to be the sum of the positive factors of n. For example, \underline{\,6\,} = 1 + 2 + 3 + 6 = 12. Find \underline{\,\underline{\,11\,}\,} .

\textbf{(A)}\ 13 \qquad \textbf{(B)}\ 20 \qquad \textbf{(C)}\ 24 \qquad \textbf{(D)}\ 28 \qquad \textbf{(E)}\ 30

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.