Sigma Function of 6

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Example of Sigma Function of Integer

$\map \sigma 6 = 12$

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


Proof

We have that:

$6 = 2 \times 3$

Hence:

\(\displaystyle \map \sigma 6\) \(=\) \(\displaystyle \paren {2 + 1} \paren {3 + 1}\) Sigma Function of Non-Square Semiprime
\(\displaystyle \) \(=\) \(\displaystyle 3 \times 4\)
\(\displaystyle \) \(=\) \(\displaystyle 2^2 \times 3\)
\(\displaystyle \) \(=\) \(\displaystyle 12\)

$\blacksquare$