Given a positive integer $k$, let $f(k)$ be the sum of the $k$-th powers of the primitive roots of $73$. For how many positive integers $k < 2015$ is $f(k)$ divisible by $73?$

[i]Note: A primitive root of $r$ of a prime $p$ is an integer $1 \le r < p$ such that the smallest positive integer $k$ such that $r^k \equiv 1 \pmod{p}$ is $k = p-1$.[/i]

Let's think step by step and output the final answer within \boxed{}.
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