Sigma Function of 2016

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Example of Sigma Function of Integer

$\map \sigma {2016} = 6552$

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


Proof

We have that:

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


Hence:

\(\ds \map \sigma {2016}\) \(=\) \(\ds \frac {2^6 - 1} {2 - 1} \times \frac {3^3 - 1} {3 - 1} \times \paren {7 + 1}\) Sigma Function of Integer
\(\ds \) \(=\) \(\ds \frac {63} 1 \times \frac {26} 2 \times 8\)
\(\ds \) \(=\) \(\ds \paren {3^2 \times 7} \times 13 \times 2^3\)
\(\ds \) \(=\) \(\ds 2^3 \times 3^2 \times 7 \times 13\)
\(\ds \) \(=\) \(\ds 6552\)

$\blacksquare$