2016 AMC 12B Problem 25

a0=1,a1=219,an=an1×an22\Large a_0 = 1, a_1 = \sqrt[19]{2}, \\ \Large a_n = a_{n-1} \times a_{n-2} ^2

Consider a sequence defined recursively for n2 n\geq 2 in the above manner.

What is the smallest positive integer value kk such that the product a1a2aka_{1}a_{2}\dotsm a_k is an integer?


Check out the whole set: 2016 AMC 12B Problems.
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