Divisor Sum of 177,792

Example of Divisor Sum of Integer

$\map {\sigma_1} {177 \, 792} = 473 \, 280$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$177 \, 792 = 2^7 \times 3 \times 7 \times 463$

Hence:

$\ds \map {\sigma_1} {177 \, 792}$

$=$

$\ds \frac {2^8 - 1} {2 - 1} \times \paren {3 + 1} \times \paren {7 + 1} \times \paren {463 + 1}$

$\ds $

$=$

$\ds 255 \times 4 \times 8 \times 464$

$\ds $

$=$

$\ds \paren {3 \times 5 \times 17} \times 2^2 \times 2^3 \times \paren {2^4 \times 29}$

$\ds $

$=$

$\ds 2^6 \times 3 \times 5 \times 17 \times 29$

$\ds $

$=$

$\ds 473 \, 280$

$\blacksquare$