Factorial factors

How many integers nn are there such that 2n1002\leq n\leq 100, and (n1)!(n-1)! is not divisible by nn?

Details and Assumptions:

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