# 2016 is absolutely awesome 2

Number Theory Level 5

$$a_0, a_1,...$$ is a sequence of positive integers where $$a_0=1; a_1=1; a_2=2; a_3=6$$.

Moreover, for all $$n \ge 4$$, $$a_n$$ is the smallest positive integer such that:

$$\dfrac{a_n}{a_ia_{n-i}}$$ is an integer for all integers $$i, 0 \le i \le n$$.

Find $$\sqrt[2016]{a_{2016}}$$.

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