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.