Originally Posted by

**I-Think** I have to find a formula for the function

$\displaystyle f(n)=\sum_{d|n}\sigma(d)$

where

$\displaystyle n=p_1^{e_1}p_2^{e_2}***p_r^{e_r}$

And I want to ensure that I understand the function correctly, so I will illustrate my understanding by examples with numbers

$\displaystyle f(12)=\sum_{d|12}\sigma(d)$

$\displaystyle f(12)=\sum_{d|n}24$

$\displaystyle f(12)=60$

2nd example

$\displaystyle f(9)=\sum_{d|9}\sigma(d)$

$\displaystyle f(n)=\sum_{d|n}13$

$\displaystyle f(9)=14$

Am I correct?