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An integer sequence defined from a variation of the Lucas–Lehmer primality test: the case of the Euler's totient function

I did a variation of the so-called Lucas–Lehmer primality test, I say this Wikipedia. I've used the Euler's totient function $$\varphi(n)=n\prod_{\substack{p\mid n\\ p\text{ prime}}}\left(1-\frac{1}{...
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