Divisor Sum of 21,105

Example of Divisor Sum of Integer

$\map {\sigma_1} {21 \, 105} = 42 \, 432$

where $\sigma_1$ denotes the Divisor sum function.

We have that:

$21 \, 105 = 3^2 \times 5 \times 7 \times 67$

Hence:

$\ds \map {\sigma_1} {21 \, 105}$

$=$

$\ds \dfrac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {7 + 1} \times \paren {67 + 1}$

$\ds $

$=$

$\ds \dfrac {26} 2 \times 6 \times 8 \times 68$

$\ds $

$=$

$\ds 13 \times 6 \times 8 \times 68$

$\ds $

$=$

$\ds 13 \times \paren {2 \times 3} \times 2^3 \times \paren {2^2 \times 17}$

$\ds $

$=$

$\ds 2^6 \times 3 \times 13 \times 17$

$\ds $

$=$

$\ds 42 \, 432$

$\blacksquare$