Divisor Sum of 28,035

Example of Divisor Sum of Integer

$\map {\sigma_1} {28 \, 035} = 56 \, 160$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$28 \, 035 = 3^2 \times 5 \times 7 \times 89$

Hence:

$\ds \map {\sigma_1} {28 \, 035}$

$=$

$\ds \dfrac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {7 + 1} \times \paren {89 + 1}$

$\ds $

$=$

$\ds \dfrac {26} 2 \times 6 \times 8 \times 90$

$\ds $

$=$

$\ds 13 \times 6 \times 8 \times 90$

$\ds $

$=$

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

$\ds $

$=$

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

$\ds $

$=$

$\ds 56 \, 160$

$\blacksquare$