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.

Inspiration

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