{"status": "success", "data": {"description_md": "Let $f$ be the unique function defined on the positive integers such that$$\\sum_{d\\mid n}d\\cdot f\\left(\\frac{n}{d}\\right)=1$$for all positive integers $n$, where the sum is taken over all positive divisors of $n$. What is $f(2023)$?\n\n$\\textbf{(A)}~-1536\\qquad\\textbf{(B)}~96\\qquad\\textbf{(C)}~108\\qquad\\textbf{(D)}~116\\qquad\\textbf{(E)}~144$\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>Let  <span class=\"katex--inline\">f</span>  be the unique function defined on the positive integers such that <span class=\"katex--display\">\\sum_{d\\mid n}d\\cdot f\\left(\\frac{n}{d}\\right)=1</span> for all positive integers  <span class=\"katex--inline\">n</span> , where the sum is taken over all positive divisors of  <span class=\"katex--inline\">n</span> . What is  <span class=\"katex--inline\">f(2023)</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}~-1536\\qquad\\textbf{(B)}~96\\qquad\\textbf{(C)}~108\\qquad\\textbf{(D)}~116\\qquad\\textbf{(E)}~144</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": 5, "problem_name": "2023 AMC 12A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc12A_p23", "prev": "/problem/23_amc12A_p21"}}