Divisor Sum of 5830

Example of Divisor Sum of Square-Free Integer

$\map {\sigma_1} {5830} = 11 \, 664$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$5830 = 2 \times 5 \times 11 \times 53$

Hence:

$\ds \map {\sigma_1} {5830}$

$=$

$\ds \paren {2 + 1} \paren {5 + 1} \paren {11 + 1} \paren {53 + 1}$

$\ds $

$=$

$\ds 3 \times 6 \times 12 \times 54$

$\ds $

$=$

$\ds 3 \times \paren {2 \times 3} \times \paren {2^2 \times 3} \times \paren {2 \times 3^3}$

$\ds $

$=$

$\ds 2^4 \times 3^6$

$\ds $

$=$

$\ds 11 \, 664$

$\blacksquare$