{"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 $r$, $\\{r(n): n \\text{ is a composite positive integer}\\}$ ?\n\n$\\textbf{(A)}\\; \\text{the set of positive integers} \\\\<br>\\textbf{(B)}\\; \\text{the set of composite positive integers} \\\\<br>\\textbf{(C)}\\; \\text{the set of even positive integers} \\\\<br>\\textbf{(D)}\\; \\text{the set of integers greater than 3} \\\\<br>\\textbf{(E)}\\; \\text{the set of integers greater than 4}$\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 \\text{ is a composite positive integer}\\}</span>  ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\; \\text{the set of positive integers} \\\\\\textbf{(B)}\\; \\text{the set of composite positive integers} \\\\\\textbf{(C)}\\; \\text{the set of even positive integers} \\\\\\textbf{(D)}\\; \\text{the set of integers greater than 3} \\\\\\textbf{(E)}\\; \\text{the set of integers greater than 4}</span> </p>&#10;<hr><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>", "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"}}