Divisor Sum of 24,255
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {24 \, 255} = 53 \, 352$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $24 \, 255 = 3^2 \times 5 \times 7^2 \times 11$
Hence:
\(\ds \map {\sigma_1} {24 \, 255}\) | \(=\) | \(\ds \dfrac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \dfrac {7^3 - 1} {7 - 1} \paren {11 + 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {26} 2 \times 6 \times \dfrac {342} 6 \times 12\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13 \times 6 \times 57 \times 12\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13 \times \paren {2 \times 3} \times \paren {3 \times 19} \paren {2^2 \times 3}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^3 \times 3^3 \times 13 \times 19\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 53 \, 352\) |
$\blacksquare$