{"status": "success", "data": {"description_md": "A positive integer is called a *perfect power* if it can be written in the form $a^b$, where $a$ and $b$ are positive integers with $b \\geq 2$. For example, $32$ and $125$ are perfect powers because $32 = 2^5$ and $125 = 5^3$.\n\nThe increasing sequence\n$$2, 3, 5, 6, 7, 10, \\ldots$$\nconsists of all positive integers which are not perfect powers. The sum of the squares of the digits of the 1000th number in this sequence is\n\n$\\text{(A)}\\ 42\\qquad\\text{(B)}\\ 26\\qquad\\text{(C)}\\ 33\\qquad\\text{(D)}\\ 18\\qquad\\text{(E)}\\ 21$\n\n___\n\n**[Pascal](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "<p>A positive integer is called a *perfect power* if it can be written in the form <span class=\"katex--inline\">a^b</span>, where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are positive integers with <span class=\"katex--inline\">b \\geq 2</span>. For example, <span class=\"katex--inline\">32</span> and <span class=\"katex--inline\">125</span> are perfect powers because <span class=\"katex--inline\">32 = 2^5</span> and <span class=\"katex--inline\">125 = 5^3</span>.</p>\n<p>The increasing sequence\n<span class=\"katex--display\">2, 3, 5, 6, 7, 10, \\ldots</span>\nconsists of all positive integers which are not perfect powers. The sum of the squares of the digits of the 1000th number in this sequence is</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 42\\qquad\\text{(B)}\\ 26\\qquad\\text{(C)}\\ 33\\qquad\\text{(D)}\\ 18\\qquad\\text{(E)}\\ 21</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Pascal</a>, by <a href=\"https://cemc.uwaterloo.ca/\">CEMC</a>, is licensed under the <a href=\"https://creativecommons.org/licenses/by-nc/3.0/\">CC BY-NC 3.0 DEED</a>. They are not affiliated with or endorse TopsOJ in any way.</strong></p>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2005 Pascal Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/05_pascal_p25", "prev": "/problem/05_pascal_p23"}}