{"status": "success", "data": {"description_md": "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 $360$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>For <span class=\"katex--inline\">n \\ge 1</span> call a finite sequence <span class=\"katex--inline\">(a_1, a_2 \\ldots a_n)</span> of positive integers progressive if <span class=\"katex--inline\">a_i &lt; a_{i+1}</span> and <span class=\"katex--inline\">a_i</span> divides <span class=\"katex--inline\">a_{i+1}</span> for all <span class=\"katex--inline\">1 \\le i \\le n-1</span>. Find the number of progressive sequences such that the sum of the terms in the sequence is equal to <span class=\"katex--inline\">360</span>.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2019 AIME II Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/19_aime_II_p13", "prev": "/problem/19_aime_II_p11"}}