Divisor Sum of 25,515

Example of Divisor Sum of Integer

$\map {\sigma_1} {25 \, 515} = 52 \, 464$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$25 \, 515 = 3^6 \times 5 \times 7$

Hence:

$\ds \map {\sigma_1} {8505}$

$=$

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

$\ds $

$=$

$\ds \dfrac {2186} 2 \times 6 \times 8$

$\ds $

$=$

$\ds 1093 \times 6 \times 8$

$\ds $

$=$

$\ds \paren {2 \times 3} \times 2^3 \times 1093$

$\ds $

$=$

$\ds 2^4 \times 3 \times 1093$

$\ds $

$=$

$\ds 52 \, 464$

$\blacksquare$