Divisor Sum of 15,435

Example of Divisor Sum of Integer

$\map {\sigma_1} {15 \, 435} = 31 \, 200$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$15 \, 435 = 3^2 \times 5 \times 7^3$

Hence:

$\ds \map {\sigma_1} {15 \, 435}$

$=$

$\ds \dfrac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \dfrac {7^4 - 1} {7 - 1}$

$\ds $

$=$

$\ds \dfrac {26} 2 \times 6 \times \dfrac {2400} 6$

$\ds $

$=$

$\ds 13 \times 6 \times 400$

$\ds $

$=$

$\ds 13 \times \paren {2 \times 3} \times \paren {2^4 \times 5^2}$

$\ds $

$=$

$\ds 2^5 \times 3 \times 5^2 \times 13$

$\ds $

$=$

$\ds 31 \, 200$

$\blacksquare$