MathDB

Progressive Sequences

Source: 2019 AIME II #12

March 22, 2019

AMCAIMEAIME II2019 AIME II2019 AMCSequences

Problem Statement

For

n \ge 1

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 all

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