Question 1-1 When any two of the positive divisors of a positive integer $n$ are added together, it is found that these sums are all different, and they are arranged from smallest to largest as $4$, $6$, $8$, $10$, $12$, $14$, $16$, $18$, $20$, $24$, $46$, $48$, $50$, $54$, $60$. Find the value of $n$.