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 \( A_{2017} \)?

×

Problem Loading...

Note Loading...

Set Loading...