# Prime Powers Dividing Factorials

For every prime number $$p$$ and non-negative integer $$k$$, define $$A_p (k)$$ to be the number of positive integers $$n$$ such that $$p^k \mid n!$$ but $$p^{k+1} \not \mid n!$$.

Let $$A_p$$ be the set of values of $$A_p (k)$$. How many (distinct) elements are there in $$A_{2017}$$?

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