5. The number $C$ is defined as the sum of all the positive integers $n$ such that $n-6$ is the second largest factor of $n$. What is the value of $11 C$ ?
Solution
308

Any integer is at most double its second largest factor. Therefore, we need only test the integers up to and including $n=12$ (which is double $n-6=6$ ) to see if each has $n-6$ as its second largest factor. Of these, only 7,9 and 12 do. These have total $C=7+9+12=28$, so $11 C=11 \times 28=308$.