{"status": "success", "data": {"description_md": "For positive integers $N$ and $k$, define $N$ to be $k$-nice if there exists a positive integer $a$ such that $a^k$ has exactly $N$ positive divisors. Find the number of positive integers less than $1000$ that are neither $7$-nice nor $8$-nice.\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 positive integers <span class=\"katex--inline\">N</span> and <span class=\"katex--inline\">k</span>, define <span class=\"katex--inline\">N</span> to be <span class=\"katex--inline\">k</span>-nice if there exists a positive integer <span class=\"katex--inline\">a</span> such that <span class=\"katex--inline\">a^k</span> has exactly <span class=\"katex--inline\">N</span> positive divisors. Find the number of positive integers less than <span class=\"katex--inline\">1000</span> that are neither <span class=\"katex--inline\">7</span>-nice nor <span class=\"katex--inline\">8</span>-nice.</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": "2016 AIME II Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/16_aime_II_p12", "prev": "/problem/16_aime_II_p10"}}