{"status": "success", "data": {"description_md": "Let $d(n)$ denote the number of positive integers that divide $n$, including $1$ and $n$. For example, $d(1)=1,d(2)=2,$ and $d(12)=6$. (This function is known as the divisor function.) Let$$f(n)=\\frac{d(n)}{\\sqrt [3]n}.$$There is a unique positive integer $N$ such that $f(N)>f(n)$ for all positive integers $n\\ne N$. What is the sum of the digits of $N?$\n\n$\\textbf{(A) }5 \\qquad \\textbf{(B) }6 \\qquad \\textbf{(C) }7 \\qquad \\textbf{(D) }8\\qquad \\textbf{(E) }9$\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": "

Let d(n) denote the number of positive integers that divide n , including 1 and n . For example, d(1)=1,d(2)=2, and d(12)=6 . (This function is known as the divisor function.) Let f(n)=\\frac{d(n)}{\\sqrt [3]n}. There is a unique positive integer N such that f(N)>f(n) for all positive integers n\\ne N . What is the sum of the digits of N?

\\textbf{(A) }5 \\qquad \\textbf{(B) }6 \\qquad \\textbf{(C) }7 \\qquad \\textbf{(D) }8\\qquad \\textbf{(E) }9

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2021 AMC 12A Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/21_amc12A_p24"}}