AMC 12A 2021 Spring Problem 25

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)=\dfrac{d(n)}{\sqrt[3]{n}}

There is a unique positive integer N such that f(N)>f(n) for all positive integers n \neq N. What is the sum of the digits of N ?

Answer Choices
A. 5
B. 6
C. 7
D. 8
E. 9