Factorial factors

Number Theory Level 4

How many integers \(n\) are there such that \(2\leq n\leq 100\), and \((n-1)!\) is not divisible by \(n\)?

Details and Assumptions:

The number \( n!\), read as n factorial, is equal to the product of all positive integers less than or equal to \(n\). For example, \( 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\).