\(a_0, a_1,...\) 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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