deletions | additions       diff --git a/section_Another_Result_begin_equation__.tex b/section_Another_Result_begin_equation__.tex  index 781651e..d0eb6ff 100644  --- a/section_Another_Result_begin_equation__.tex  +++ b/section_Another_Result_begin_equation__.tex 
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such that \begin{equation}  T\sum_{p\in\mathbb{P}} x^p \to \sum_{q=1}^\infty \sum_{p\in\mathbb{P}} \frac{x^{p q}}{q} = \sum_{k=2}^\infty \frac{\mathrm{sopf}(k)x^k}{k}   \end{equation}  where $\mathrm{sopf}(k)$ is the sum of the prime factors of $k$.  \begin{equation}  \sum_{q=1}^\infty \sum_{k=1}^\infty \frac{x^{p_{q k}}}{q} =\sum_{k=1}^\infty \frac{\sigma_1(k)x^{p_k}}{k}  \end{equation}