{"status": "success", "data": {"description_md": "For any positive integer $a,$ $\\sigma(a)$ denotes the sum of the positive integer divisors of $a.$ Let $n$ be the least positive integer such that $\\sigma(a^n)-1$ is divisible by $2021$ for all positive integers $a.$ Find the sum of the prime factors in the prime factorization of $n.$\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 any positive integer <span class=\"katex--inline\">a,</span> <span class=\"katex--inline\">\\sigma(a)</span> denotes the sum of the positive integer divisors of <span class=\"katex--inline\">a.</span> Let <span class=\"katex--inline\">n</span> be the least positive integer such that <span class=\"katex--inline\">\\sigma(a^n)-1</span> is divisible by <span class=\"katex--inline\">2021</span> for all positive integers <span class=\"katex--inline\">a.</span> Find the sum of the prime factors in the prime factorization of <span class=\"katex--inline\">n.</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": 6, "problem_name": "2021 AIME I Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/21_aime_I_p15", "prev": "/problem/21_aime_I_p13"}}