
\documentclass{article}


\begin{document}

\begin{rawhtml}
<h1 align=center> The Euler function
</h1>
\end{rawhtml}



The Euler function $\phi (n)$ is defined as the number of positive integers not exceeding $n$ and coprime with $n$. Also, let $N_k$ be the product of the first $k$ prime numbers, and $\gamma$ be Euler's constant.

Then RH is equivalent to each of the following statements :

$$
\frac{N_k}{\phi(N_k)} > e^{\gamma} \log \log N_k,
$$
for all $k$'s ;

$$
\frac{N_k}{\phi(N_k)} > e^{\gamma} \log \log N_k,
$$
for all but finitely many $k$'s.
 
This is due to Nicolas [
\begin{rawhtml}
<a href="http://www.ams.org/msnmain?fn=130&s1=85h:11053&pg1=MR">MR 85h:11053</a>
\end{rawhtml}].\begin{rawhtml}
<p> <br>
<hr>
<p> <br>
Back to the 
<a href="http://www.aimath.org/WWN/rh/"> main index</a> 
for The Riemann Hypothesis.
\end{rawhtml}

\end{document}

