Question 12
For $n \ge 1$ call a finite sequence $(a_1, a_2, \ldots, a_n)$ of positive integers *progressive* if $a_i \lt a_{i+1}$ and $a_i$ divides $a_{i+1}$ for $1 \le i \le n - 1.$ Find the number of progressive sequences such that the sum of the terms in the sequence is equal to $360.$