Divisor Sum of 122,410
Jump to navigation
Jump to search
Example of Divisor Sum of Integer
- $\map {\sigma_1} {122 \, 410} = 220 \, 356$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $122 \, 410 = 2 \times 5 \times 12 \, 241$
Hence:
\(\ds \map {\sigma_1} {122 \, 410}\) | \(=\) | \(\ds \paren {2 + 1} \times \paren {5 + 1} \times \paren {12 \, 241 + 1}\) | Divisor Sum of Square-Free Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times 6 \times 12 \, 242\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times \paren {2 \times 3} \times \paren {2 \times 6121}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^2 \times 3^2 \times 6121\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 220 \, 356\) |
$\blacksquare$