Why is the following estimation true ?
$\displaystyle\sum\limits_{h_1,k_1\atop p|h_1k_1\implies p\le Y}\frac{e^{\Omega(h_1)}}{lcm(h_1,k_1)}\ll\prod\limits_{p\le Y}\left(1+\frac{1+2e}{p}\right)$
, where $\Omega(h_1)$ is the number of prime factors (including repetition) of $h_1$
The original estimation below looks a bit different with exponent $\sigma_0\ge\frac12$ and Möbius-function, but this does not change much;
