Floor and Factorial

Number Theory Level 4

\[\large\left\lfloor \frac { x }{ 1! } \right\rfloor +\left\lfloor \frac { x }{ 2! } \right\rfloor +\left\lfloor \frac { x }{ 3! } \right\rfloor =n\]

Let \(x\) be integer. The integer \(n\) is achievable if there exists \(x\) satisfying the equation, otherwise it is NOT achievable.

How many positive integers \(n\), where \(1\le n \le 2016\), is achievable?

Note: \(n=224\) is achievable while \(n=222\) is NOT achievable.



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