Divisor Sum of 19,845

Example of Divisor Sum of Integer

$\map {\sigma_1} {19 \, 845} = 41 \, 382$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$19 \, 845 = 3^4 \times 5 \times 7^2$

Hence:

$\ds \map {\sigma_1} {19 \, 845}$

$=$

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

$\ds $

$=$

$\ds \dfrac {242} 2 \times 6 \times \dfrac {342} 6$

$\ds $

$=$

$\ds 121 \times 6 \times 57$

$\ds $

$=$

$\ds 11^2 \times \paren {2 \times 3} \times \paren {3 \times 19}$

$\ds $

$=$

$\ds 2 \times 3^2 \times 11^2 \times 19$

$\ds $

$=$

$\ds 41 \, 382$

$\blacksquare$