# Factorial Divisibility (E)

**Number Theory**Level 4

For how many natural numbers \( n < 1000 \) does \( n \not | (n-1)! \)?

**Details and Assumptions**

\( n! \) is the factorial function where \( n! = n*(n-1)! \) and \( 0! = 1 \).

\( a \not | b \) means that \( a \) does not perfectly divide \(b \), i.e. \( a \) is not a divisor of \( b \).For example, \( 20 \not | 75 \).

You may use the List of Primes as a reference.