Checking the divisibility of a factorial
When Madin learnt about factorials, he was delighted that they had so many factors since \( k! = 1 \times 2 \times 3 \times \ldots \times k \). He knew that \(k!\) would be divisible by any positive integer that was smaller than \(k\), but wasn't certain about the larger integers.
Can you find the number of integers \(n\) such that \(2\leq n\leq 100\) and \((n-1)!\) is not divisible by \(n^2\)?