Formula:8117

Digital Library of Mathematical Functions ID 24.4.E11

${\displaystyle{\displaystyle\sum_{\begin{subarray}{c}k=1\\ \left(k,m\right)=1\end{subarray}}^{m}k^{n}=\frac{1}{n+1}\sum_{j=1}^{n+1}{n+1\choose j}\*\left(\prod_{p\mathbin{|}m}(1-p^{n-j})B_{n+1-j}\right)m^{j}.}}$

Symbols List

• ${\displaystyle{\displaystyle B_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle\left(\NVar{m},\NVar{n}\right)}}$:
• ${\displaystyle{\displaystyle j}}$: integer
• ${\displaystyle{\displaystyle k}}$: integer
• ${\displaystyle{\displaystyle m}}$: integer
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle p}}$: prime
 

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