Sigma Function of 6368

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Example of Sigma Function of Integer

$\sigma \left({6368}\right) = 12 \, 600$

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


Proof

From Sigma Function of Integer

$\displaystyle \sigma \left({n}\right) = \prod_{1 \mathop \le i \mathop \le r} \frac {p_i^{k_i + 1} - 1} {p_i - 1}$

where $n = \displaystyle \prod_{1 \mathop \le i \mathop \le r} p_i^{k_i}$ denotes the prime decomposition of $n$.


We have that:

$6368 = 2^5 \times 199$


Hence:

\(\displaystyle \sigma \left({6368}\right)\) \(=\) \(\displaystyle \frac {2^6 - 1} {2 - 1} \times \left({199 + 1}\right)\)
\(\displaystyle \) \(=\) \(\displaystyle \frac {63} 1 \times 200\)
\(\displaystyle \) \(=\) \(\displaystyle \left({3^2 \times 7}\right) \times \left({2^3 \times 5^2}\right)\)
\(\displaystyle \) \(=\) \(\displaystyle 2^3 \times 3^2 \times 5^2 \times 7\)
\(\displaystyle \) \(=\) \(\displaystyle 12 \, 600\)

$\blacksquare$