Question 9
Denote the number of positive factors of an integer $n$ by $F(n)$. For example, the positive factors of $12$ are $1,2,3,4,6,12$, so $F(12)=6$. In addition, the positive factors of $6$ are $1,2,3,6$, so $F(F(12))=4$. If $F(F(n))=3$ and $F(F(6n))=7$, find $F(n)$.