Grinding Aces Math Exam 2025 - Problem 5

For any positive integer $n\ge 2$ let $d(n)$ denote the number of positive divisor of $n$ and $\phi(n)$ denote the number of positive integers from $1$ to $n$ inclusive relatively prime with $n$. Let $\nu_p(n)$ denote the largest value $k$ such that $p^k$ divides $n$. Given that $N$ is a positive integer for which $d(N)=2025$, let the minimum value of $\phi(N)$ be $x$. Find

$\sum_{p \text{ is prime}}{\nu_p(x)}$