Divisor Sum of 47,616

Example of Divisor Sum of Integer

$\map {\sigma_1} {47 \, 616} = 130 \, 994$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$47 \, 616 = 2^9 \times 3 \times 31$

Hence:

$\ds \map {\sigma_1} {47 \, 616}$

$=$

$\ds \frac {2^{10} - 1} {2 - 1} \times \paren {3 + 1} \times \paren {31 + 1}$

$\ds $

$=$

$\ds 1023 \times 4 \times 32$

$\ds $

$=$

$\ds \paren {3 \times 11 \times 31} \times 2^2 \times 2^5$

$\ds $

$=$

$\ds 2^7 \times 3 \times 11 \times 31$

$\ds $

$=$

$\ds 130 \, 994$

$\blacksquare$