{"status": "success", "data": {"description_md": "For every composite positive integer $n$, define $r(n)$ to be the sum of the factors in the prime factorization of $n$. For example, $r(50) = 12$ because the prime factorization of $50$ is $2 \\times 5^2$, and $2 + 5 + 5 = 12$. What is the range of the function $r$, $\\{r(n): n$ is a composite positive integer$\\}$ ?\n\n$\\mathrm{(A) \\ } \\text{the set of positive integers} \\qquad \\mathrm{(B) \\text{the set of composite positive integers} \\ } \\qquad \\mathrm{(C) \\text{the set of even positive integers}}\\qquad \\mathrm{(D) \\text{the set of integers greater than 3}} \\qquad \\mathrm{(E) \\text{the set of integers greater than 4}}$\n___\nFull 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 every composite positive integer <span class=\"katex--inline\">n</span>, define <span class=\"katex--inline\">r(n)</span> to be the sum of the factors in the prime factorization of <span class=\"katex--inline\">n</span>. For example, <span class=\"katex--inline\">r(50) = 12</span> because the prime factorization of <span class=\"katex--inline\">50</span> is <span class=\"katex--inline\">2 \\times 5^2</span>, and <span class=\"katex--inline\">2 + 5 + 5 = 12</span>. What is the range of the function <span class=\"katex--inline\">r</span>, <span class=\"katex--inline\">\\{r(n): n</span> is a composite positive integer<span class=\"katex--inline\">\\}</span> ?</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A) \\ } \\text{the set of positive integers} \\qquad \\mathrm{(B) \\text{the set of composite positive integers} \\ } \\qquad \\mathrm{(C) \\text{the set of even positive integers}}\\qquad \\mathrm{(D) \\text{the set of integers greater than 3}} \\qquad \\mathrm{(E) \\text{the set of integers greater than 4}}</span></p>&#10;<hr/>&#10;<p>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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2015 AMC 12B Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/15_amc12B_p19", "prev": "/problem/15_amc12B_p17"}}