Sigma Function of Integer/Examples/12

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Example of Sigma Function of Integer

$\sigma \left({12}\right) = 28$

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


Proof

We have that:

$12 = 2^2 \times 3$


Hence:

\(\displaystyle \sigma \left({12}\right)\) \(=\) \(\displaystyle \frac {2^3 - 1} {2 - 1} \times \left({3 + 1}\right)\) Sigma Function of Integer
\(\displaystyle \) \(=\) \(\displaystyle \frac 7 1 \times 4\)
\(\displaystyle \) \(=\) \(\displaystyle 7 \times 4\)
\(\displaystyle \) \(=\) \(\displaystyle 28\)

$\blacksquare$