Factorial Divisibility (E)

For how many natural numbers n<1000 n < 1000 does n∤(n1)! n \not | (n-1)! ?

Details and Assumptions

  • n! n! is the factorial function where n!=n(n1)! n! = n*(n-1)! and 0!=1 0! = 1 .

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

  • You may use the List of Primes as a reference.

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