Sigma Function of 720

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Example of Sigma Function of Integer

$\sigma \left({720}\right) = 2418$

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


Proof

We have that:

$720 = 2^4 \times 3^2 \times 5$

Hence:

\(\displaystyle \sigma \left({720}\right)\) \(=\) \(\displaystyle \frac {2^5 - 1} {2 - 1} \times \frac {3^3 - 1} {3 - 1} \times \left({5 + 1}\right)\) Sigma Function of Integer
\(\displaystyle \) \(=\) \(\displaystyle \frac {31} 1 \times \frac {26} 2 \times 6\)
\(\displaystyle \) \(=\) \(\displaystyle 31 \times 13 \times \left({2 \times 3}\right)\)
\(\displaystyle \) \(=\) \(\displaystyle 2 \times 3 \times 13 \times 31\)
\(\displaystyle \) \(=\) \(\displaystyle 2418\)

$\blacksquare$