# 2022-22 An integral sequence

Define a sequence $$a_n$$ by $$a_1 = 1$$ and
$a_{n+1} = \frac{1}{n} \left( 1 + \sum_{k=1}^n a_k^2 \right)$
for any $$n \geq 1$$. Prove or disprove that $$a_n$$ is an integer for all $$n \geq 1$$.

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