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4
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Quick question: It's known that $$\limsup\frac{n}{\varphi(n)\log\log n}=e^\gamma$$ but are there known C and N such that $$\varphi(n)>\frac{Cn}{e^\gamma\log\log n}$$ for all $n>N$? Failing that, what are good effective bounds on $\varphi$? The square root bound isn't good enough for me. |
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6
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Yes. Look at http://en.wikipedia.org/wiki/Euler's_totient_function#Inequalities: $$\varphi(n)>\frac{n}{e^\gamma\log\log n + \frac{3}{\log\log n}}$$ for $n>2$. |
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