Divisor Sum of 5775
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {5775} = 11 \, 904$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $5775 = 3 \times 5^2 \times 7 \times 11$
Hence:
\(\ds \map {\sigma_1} {5775}\) | \(=\) | \(\ds \paren {3 + 1} \times \dfrac {5^3 - 1} {5 - 1} \times \paren {7 + 1} \times \paren {11 + 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds 4 \times \dfrac {124} 4 \times 8 \times 12\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 4 \times 31 \times 8 \times 12\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^2 \times 31 \times 2^3 \times \paren {2^2 \times 3}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^7 \times 3 \times 31\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 11 \, 904\) |
$\blacksquare$