# Factorial Divisibility (E)

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.

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