# Divisor Sum of 30

## Example of Divisor Sum of Square-Free Integer

$\map {\sigma_1} {30} = 72$

where $\sigma_1$ denotes the divisor sum function.

## Proof

We have that:

$30 = 2 \times 3 \times 5$

Hence:

 $\ds \map {\sigma_1} {30}$ $=$ $\ds \paren {2 + 1} \paren {3 + 1} \paren {5 + 1}$ Divisor Sum of Square-Free Integer $\ds$ $=$ $\ds 3 \times 4 \times 6$ $\ds$ $=$ $\ds 3 \times 2^2 \times \paren {2 \times 3}$ $\ds$ $=$ $\ds 2^3 \times 3^2$ $\ds$ $=$ $\ds 72$

$\blacksquare$