Divisor Sum of 33,705

Example of Divisor Sum of Integer

$\map {\sigma_1} {33 \, 705} = 67 \, 392$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$33 \, 705 = 3^2 \times 5 \times 7 \times 107$

Hence:

$\ds \map {\sigma_1} {33 \, 705}$

$=$

$\ds \dfrac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {7 + 1} \times \paren {107 + 1}$

$\ds $

$=$

$\ds \dfrac {26} 2 \times 6 \times 8 \times 108$

$\ds $

$=$

$\ds 13 \times 6 \times 8 \times 108$

$\ds $

$=$

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

$\ds $

$=$

$\ds 2^6 \times 3^4 \times 13$

$\ds $

$=$

$\ds 67 \, 392$

$\blacksquare$