Divisor Sum of 1034
Jump to navigation
Jump to search
Example of Divisor Sum of Square-Free Integer
- $\map {\sigma_1} {1034} = 1728$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $1034 = 2 \times 11 \times 47$
Hence:
\(\ds \map {\sigma_1} {994}\) | \(=\) | \(\ds \paren {2 + 1} \paren {11 + 1} \paren {47 + 1}\) | Divisor Sum of Square-Free Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times 12 \times 48\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times \paren {2^2 \times 3} \times \paren {2^3 \times 3}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^6 \times 3^3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {2^2 \times 3}^3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 1728\) |
$\blacksquare$