# Sigma Function of 2016

## Example of Sigma Function of Integer

$\sigma \left({2016}\right) = 6552$

where $\sigma$ denotes the $\sigma$ function.

## Proof

We have that:

$2016 = 2^5 \times 3^2 \times 7$

Hence:

 $\displaystyle \sigma \left({2016}\right)$ $=$ $\displaystyle \frac {2^6 - 1} {2 - 1} \times \frac {3^3 - 1} {3 - 1} \times \left({7 + 1}\right)$ Sigma Function of Integer $\displaystyle$ $=$ $\displaystyle \frac {63} 1 \times \frac {26} 2 \times 8$ $\displaystyle$ $=$ $\displaystyle \left({3^2 \times 7}\right) \times 13 \times 2^3$ $\displaystyle$ $=$ $\displaystyle 2^3 \times 3^2 \times 7 \times 13$ $\displaystyle$ $=$ $\displaystyle 6552$

$\blacksquare$