Question 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 $$
f(n) = \frac{d(n)}{\sqrt[3]{n}}.
$$
There is a unique positive integer $N$ such that $f(N) \gt f(n)$ for all positive integers $n \ne N.$ What is the sum of the digits of $N?$
f(n) = \frac{d(n)}{\sqrt[3]{n}}.
$$
There is a unique positive integer $N$ such that $f(N) \gt f(n)$ for all positive integers $n \ne N.$ What is the sum of the digits of $N?$