Divisor Sum of 27,405

Example of Divisor Sum of Integer

$\map {\sigma_1} {27 \, 405} = 57 \, 600$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$27 \, 405 = 3^3 \times 5 \times 7 \times 29$

Hence:

$\ds \map {\sigma_1} {27 \, 405}$

$=$

$\ds \dfrac {3^4 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {7 + 1} \times \paren {29 + 1}$

$\ds $

$=$

$\ds \dfrac {80} 2 \times 6 \times 8 \times 30$

$\ds $

$=$

$\ds 40 \times 6 \times 8 \times 30$

$\ds $

$=$

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

$\ds $

$=$

$\ds 2^8 \times 3^2 \times 5^2$

$\ds $

$=$

$\ds 57 \, 600$

$\blacksquare$