Formula:8731

Digital Library of Mathematical Functions ID 27.6.E6

${\displaystyle{\displaystyle\sum_{d\mathbin{|}n}\phi_{k}\left(d\right)\left(\frac{n}{d}\right)^{k}=1^{k}+2^{k}+\dots+n^{k},}}$

Symbols List

• ${\displaystyle{\displaystyle\phi_{\NVar{k}}\left(\NVar{n}\right)}}$: sum of powers of integers relatively prime to $$n$$
• ${\displaystyle{\displaystyle d}}$: positive integer
• ${\displaystyle{\displaystyle k}}$: positive integer
• ${\displaystyle{\displaystyle n}}$: positive integer
 

Resources that cite this formula

No records found.