Divisor Sum of 770

Example of Divisor Sum of Square-Free Integer

$\map {\sigma_1} {770} = 1728$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$770 = 2 \times 5 \times 7 \times 11$

Hence:

$\ds \map {\sigma_1} {770}$

$=$

$\ds \paren {2 + 1} \paren {5 + 1} \paren {7 + 1} \paren {11 + 1}$

$\ds $

$=$

$\ds 3 \times 6 \times 8 \times 12$

$\ds $

$=$

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

$\ds $

$=$

$\ds 2^6 \times 3^4$

$\ds $

$=$

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

$\ds $

$=$

$\ds 1728$

$\blacksquare$