2019 AIME II Problem 12

For n\ge1 call a finite sequence (a_1,a_2,\ldots,a_n) of positive integers *progressive* if a_i<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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.