Divisor Sum of 21,735
Jump to navigation
Jump to search
Example of Divisor Sum of Integer
- $\map {\sigma_1} {21 \, 735} = 46 \, 080$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $21 \, 735 = 3^3 \times 5 \times 7 \times 23$
Hence:
\(\ds \map {\sigma_1} {21 \, 735}\) | \(=\) | \(\ds \dfrac {3^4 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {7 + 1} \times \paren {23 + 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {80} 2 \times 6 \times 8 \times 24\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 40 \times 6 \times 8 \times 24\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {2^3 \times 5} \times \paren {2 \times 3} \times 2^3 \times \paren {2^3 \times 3}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^10 \times 3^2 \times 5\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 46 \, 080\) |
$\blacksquare$