Formula:8700

Digital Library of Mathematical Functions ID 27.3.E6

${\displaystyle{\displaystyle\sigma_{\alpha}\left(n\right)=\prod_{r=1}^{\nu\left(n\right)}\frac{p^{\alpha(1+a_{r})}_{r}-1}{p^{\alpha}_{r}-1},}}$

Constraint(s)

${\displaystyle{\displaystyle\alpha\neq 0}}$

Symbols List

• ${\displaystyle{\displaystyle\sigma_{\NVar{\alpha}}\left(\NVar{n}\right)}}$: sum of powers of divisors of $$n$$
• ${\displaystyle{\displaystyle\nu\left(\NVar{n}\right)}}$:
• ${\displaystyle{\displaystyle n}}$: positive integer
• ${\displaystyle{\displaystyle p,p_{1},\ldots}}$: prime numbers
• ${\displaystyle{\displaystyle a_{r}}}$: primitive root
 

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