Divisor Sum of 523,776

Example of Divisor Sum of Integer

$\map {\sigma_1} {523 \, 776} = 1 \, 571 \, 328$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$523 \, 776 = 2^9 \times 3 \times 11 \times 31$

Hence:

$\ds \map {\sigma_1} {523 \, 776}$

$=$

$\ds \frac {2^{10} - 1} {2 - 1} \times \paren {3 + 1} \times \paren {11 + 1} \times \paren {31 + 1}$

$\ds $

$=$

$\ds 1023 \times 4 \times 12 \times 32$

$\ds $

$=$

$\ds \paren {3 \times 11 \times 31} \times 2^2 \times \paren {2^2 \times 3} \times 2^5$

$\ds $

$=$

$\ds 2^9 \times 3^2 \times 11 \times 31$

$\ds $

$=$

$\ds 3 \times \paren {2^9 \times 3 \times 11 \times 31}$

$\ds $

$=$

$\ds 1 \, 571 \, 328$

$\blacksquare$