Formula:8732

Digital Library of Mathematical Functions ID 27.6.E7

${\displaystyle{\displaystyle\sum_{d\mathbin{|}n}\mu\left(d\right)\left(\frac{n}{d}\right)^{k}=J_{k}\left(n\right),}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{k}}\left(\NVar{n}\right)}}$: Jordan’s function
• ${\displaystyle{\displaystyle\mu\left(\NVar{n}\right)}}$: Möbius function
• ${\displaystyle{\displaystyle d}}$: positive integer
• ${\displaystyle{\displaystyle k}}$: positive integer
• ${\displaystyle{\displaystyle n}}$: positive integer
 

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