2019 AIME II Problem 12

For n \geq 1 call a finite sequence \left(a_{1}, a_{2} \ldots a_{n}\right) of positive integers progressive if a_{i}<a_{i+1} and a_{i} divides a_{i+1} for all 1 \leq i \leq n-1. Find the number of progressive sequences such that the sum of the terms in the sequence is equal to 360 .