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If $\phi(n)$ is the Euler-totient function, how can I show that $\phi(n) \ge \sqrt{n}$?

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$\varphi(2)=1<\sqrt2$. – Brian M. Scott Feb 20 '13 at 2:00
I'm sure this question has been asked, and answered, here, but I'm not sure how to find it. – Gerry Myerson Feb 20 '13 at 2:01
$\varphi(6) = 2 < \sqrt{6}$ – mixedmath Feb 20 '13 at 2:01
See, for example,… --- especially Brian's answer. – Gerry Myerson Feb 20 '13 at 2:08
@Gerry,… – Will Jagy Feb 20 '13 at 2:08

Hint: both $\phi(n)$ and $\sqrt{n}$ are multiplicative, so it suffices to consider prime powers.

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