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4.3: Inversión de Mobius
https://espanol.libretexts.org/Matematicas/Combinatoria_y_Matematicas_Discretas/Una_introducci%C3%B3n_a_la_teor%C3%ADa_de_n%C3%BAmeros_(Veerman)/04%3A_Funciones_te%C3%B3ricas_num%C3%A9ricas/4.03%3A_Inversi%C3%B3n_de_Mobius
$ab = \left. \begin{array} {ab = d}\\ {d|n} \end{array} \right \} \Rightarrow b|n \mbox{ and } a | \frac{n}{d} \nonumber$ \[f(d) = \sum_{a|d} \mu (a) F\left(\frac{d}{a}\right) = \sum_{\{(a,b) | ab =... $ab = \left. \begin{array} {ab = d}\\ {d|n} \end{array} \right \} \Rightarrow b|n \mbox{ and } a | \frac{n}{d} \nonumber$ $f(d) = \sum_{a|d} \mu (a) F\left(\frac{d}{a}\right) = \sum_{\{(a,b) | ab = d\}} \mu (a) F(b) \nonumber$ $H(n) \equiv \sum_{d|n} f(d) = \sum_{d|n} \sum_{a|d} \mu (a) F(\frac{d}{a}) \nonumber$ $H(n) = \sum_{b|n} \sum_{a|(\frac{n}{b})} \mu (a) F(b) = \sum_{b|n} \left(\sum_{a| \frac{n}{b}} \mu (a)\right) F(b) \nonumber$

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