$g(n)$ is an arithmetic function such that: $g(ab) = g(a)g(b)$ for all natural $a, b$ and $g(p)=p+2023$ where $p$ is prime. $g(1)=2024$. $f(n)$ is an arithmetic function such that the sum of $f$ of every divisor of $n$ is equal to $g(n)$. E.g. $g(1234567)$ = $f(1)$ + $f(127)$ + $f(9721)$ + $f(1234567)$. Find the number of divisors of $f(7^{17})$.