Divisor Sum of 22,976

Example of Divisor Sum of Integer

$\map {\sigma_1} {22 \, 976} = 45 \, 720$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$22 \, 976 = 2^6 \times 359$

Hence:

$\ds \map {\sigma_1} {22 \, 976}$

$=$

$\ds \frac {2^7 - 1} {2 - 1} \times \paren {359 + 1}$

$\ds $

$=$

$\ds 127 \times 360$

$\ds $

$=$

$\ds 127 \times \paren {2^3 \times 3^2 \times 5}$

$\ds $

$=$

$\ds 2^3 \times 3^2 \times 5 \times 127$

$\ds $

$=$

$\ds 45 \, 720$

$\blacksquare$