Divisor Sum of 22,744

Example of Divisor Sum of Integer

$\map {\sigma_1} {22 \, 744} = 42 \, 660$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$22 \, 744 = 2^3 \times 2843$

Hence:

$\ds \map {\sigma_1} {22 \, 744}$

$=$

$\ds \frac {2^4 - 1} {2 - 1} \times \paren {2843 + 1}$

$\ds $

$=$

$\ds 15 \times 2844$

$\ds $

$=$

$\ds \paren {3 \times 5} \times \paren {2^2 \times 3^2 \times 79}$

$\ds $

$=$

$\ds 2^2 \times 3^3 \times 5 \times 79$

$\ds $

$=$

$\ds 42 \, 660$

$\blacksquare$