calculus - $mathop {lim }limits_{n to infty } ,frac{{tan (n)}}{{{n^k}}}$

what is the minimum number of $k$ for which the following limit exist
$$\mathop {\lim }\limits_{n \to \infty } \,\frac{{\tan (n)}}{{{n^k}}}$$
I know that $$\mathop {\lim }\limits_{n \to \infty } \,\frac{{\tan (n)}}{n}$$
doesn't exist, and $$\mathop {\lim }\limits_{n \to \infty } \,\frac{{\tan (n)}}{{{n^8}}} = 0.$$
But i don't know what is the minimum number of $k$ for existing that limit.
(note that here n's are positive integers not real numbers)