Divisor Sum of 33,075
Jump to navigation
Jump to search
Example of Divisor Sum of Integer
- $\map {\sigma_1} {33 \, 075} = 70 \, 680$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $33 \, 075 = 3^3 \times 5^2 \times 7^2$
Hence:
\(\ds \map {\sigma_1} {33 \, 075}\) | \(=\) | \(\ds \dfrac {3^4 - 1} {3 - 1} \times \dfrac {5^3 - 1} {5 - 1} \times \dfrac {7^3 - 1} {7 - 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {80} 2 \times \dfrac {124} 4 \times \dfrac {342} 6\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 40 \times 31 \times 57\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {2^3 \times 5} \times 31 \times \paren {3 \times 19}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^3 \times 3 \times 5 \times 19 \times 31\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 70 \, 680\) |
$\blacksquare$