Divisor Sum of 1980

Example of Divisor Sum of Integer

$\map {\sigma_1} {1980} = 6552$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$1980 = 2^2 \times 3^2 \times 5 \times 11$

Hence:

$\ds \map {\sigma_1} {1980}$

$=$

$\ds \frac {2^3 - 1} {2 - 1} \times \frac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {11 + 1}$

$\ds $

$=$

$\ds \frac 7 1 \times \frac {26} 2 \times 6 \times 12$

$\ds $

$=$

$\ds 7 \times 13 \times \paren {2 \times 3} \times \paren {2^2 \times 3}$

$\ds $

$=$

$\ds 2^3 \times 3^2 \times 7 \times 13$

$\ds $

$=$

$\ds 6552$

$\blacksquare$