Divisor Sum of 2556
Jump to navigation
Jump to search
Example of Divisor Sum of Integer
- $\map {\sigma_1} {2556} = 6552$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $2556 = 2^2 \times 3^2 \times 71$
Hence:
\(\ds \map {\sigma_1} {2556}\) | \(=\) | \(\ds \frac {2^3 - 1} {2 - 1} \times \frac {3^3 - 1} {3 - 1} \times \paren {71 + 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac 7 1 \times \frac {26} 2 \times 72\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 7 \times 13 \times \paren {2^3 \times 3^2}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^3 \times 3^2 \times 7 \times 13\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 6552\) |
$\blacksquare$