Sigma Function of 1,438,983

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Example of Sigma Function of Integer

$\sigma \left({1 \, 438 \, 983}\right) = 2 \, 614 \, 248$

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


Proof

We have that:

$1 \, 438 \, 983 = 3^2 \times 7^2 \times 13 \times 251$


Hence from Sigma Function of Integer:

\(\ds \sigma \left({1 \, 438 \, 983}\right)\) \(=\) \(\ds \frac {3^3 - 1} {3 - 1} \times \frac {7^3 - 1} {7 - 1} \times \left({13 + 1}\right) \times \left({251 + 1}\right)\)
\(\ds \) \(=\) \(\ds \frac {26} 2 \times \frac {342} 6 \times 14 \times 252\)
\(\ds \) \(=\) \(\ds 13 \times 57 \times 14 \times 252\)
\(\ds \) \(=\) \(\ds 13 \times \times \left({3 \times 19}\right) \times \left({2 \times 7}\right) \times \left({2^2 \times 3^2 \times 7}\right)\)
\(\ds \) \(=\) \(\ds 2^3 \times 3^3 \times 7^2 \times 13 \times 19\)
\(\ds \) \(=\) \(\ds 2 \, 614 \, 248\)

$\blacksquare$