Divisor Sum of 22,365

Example of Divisor Sum of Integer

$\map {\sigma_1} {22 \, 365} = 44 \, 928$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$22 \, 365 = 3^2 \times 5 \times 7 \times 71$

Hence:

$\ds \map {\sigma_1} {22 \, 365}$

$=$

$\ds \dfrac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {7 + 1} \times \paren {71 + 1}$

$\ds $

$=$

$\ds \dfrac {26} 2 \times 6 \times 8 \times 72$

$\ds $

$=$

$\ds 13 \times 6 \times 8 \times 72$

$\ds $

$=$

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

$\ds $

$=$

$\ds 2^7 \times 3^3 \times 13$

$\ds $

$=$

$\ds 44 \, 928$

$\blacksquare$