Divisor Sum of 23,625
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {23 \, 625} = 49 \, 920$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $23 \, 625 = 3^3 \times 5^3 \times 7$
Hence:
\(\ds \map {\sigma_1} {23 \, 625}\) | \(=\) | \(\ds \dfrac {3^4 - 1} {3 - 1} \times \dfrac {5^4 - 1} {5 - 1} \times \paren {7 + 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {80} 2 \times \dfrac {624} 4 \times 8\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 40 \times 156 \times 8\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {2^3 \times 5} \times \paren {2^2 \times 3 \times 13} \times 2^3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^8 \times 3 \times 5 \times 13\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 49 \, 920\) |
$\blacksquare$