Divisor Sum of 8085

Example of Divisor Sum of Integer

$\map {\sigma_1} {8085} = 16 \, 416$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$8085 = 3 \times 5 \times 7^2 \times 11$

Hence:

$\ds \map {\sigma_1} {8085}$

$=$

$\ds \paren {3 + 1} \times \paren {5 + 1} \times \dfrac {7^3 - 1} {7 - 1} \times \paren {11 + 1}$

$\ds $

$=$

$\ds 4 \times 6 \times \dfrac {342} 6 \times 12$

$\ds $

$=$

$\ds 4 \times 6 \times 57 \times 12$

$\ds $

$=$

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

$\ds $

$=$

$\ds 2^5 \times 3^3 \times 19$

$\ds $

$=$

$\ds 16 \, 416$

$\blacksquare$