Divisor Sum of 18,585

Example of Divisor Sum of Integer

$\map {\sigma_1} {18 \, 585} = 33 \, 696$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$18 \, 585 = 3^2 \times 5 \times 7 \times 59$

Hence:

$\ds \map {\sigma_1} {18 \, 585}$

$=$

$\ds \dfrac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {7 + 1} \times \paren {59 + 1}$

$\ds $

$=$

$\ds \dfrac {26} 2 \times 6 \times 8 \times 60$

$\ds $

$=$

$\ds 13 \times 6 \times 8 \times 60$

$\ds $

$=$

$\ds 13 \times \paren {2 \times 3} \times 2^3 \times \paren {2^2 \times 3 \times 5}$

$\ds $

$=$

$\ds 2^6 \times 3^2 \times 5 \times 13$

$\ds $

$=$

$\ds 37 \, 440$

$\blacksquare$