Sigma Function of 1980

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Example of Sigma Function of Integer

$\sigma \left({1980}\right) = 6552$

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


Proof

We have that:

$1980 = 2^2 \times 3^2 \times 5 \times 11$

Hence:

\(\displaystyle \sigma \left({1980}\right)\) \(=\) \(\displaystyle \frac {2^3 - 1} {2 - 1} \times \frac {3^3 - 1} {3 - 1} \times \left({5 + 1}\right) \times \left({11 + 1}\right)\) Sigma Function of Integer
\(\displaystyle \) \(=\) \(\displaystyle \frac 7 1 \times \frac {26} 2 \times 6 \times 12\)
\(\displaystyle \) \(=\) \(\displaystyle 7 \times 13 \times \left({2 \times 3}\right) \times \left({2^2 \times 3}\right)\)
\(\displaystyle \) \(=\) \(\displaystyle 2^3 \times 3^2 \times 7 \times 13\)
\(\displaystyle \) \(=\) \(\displaystyle 6552\)

$\blacksquare$