Divisor Sum of 152,990
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {152 \, 990} = 275 \, 400$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $152 \, 990 = 2 \times 5 \times 15 \, 299$
Hence:
\(\ds \map {\sigma_1} {152 \, 990}\) | \(=\) | \(\ds \paren {2 + 1} \times \paren {5 + 1} \times \paren {15 \, 299 + 1}\) | Divisor Sum of Square-Free Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times 6 \times 15 \, 300\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times \paren {2 \times 3} \times \paren {2^2 \times 3^2 \times 5^2 \times 17}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^3 \times 3^4 \times 5^2 \times 17\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 275 \, 400\) |
$\blacksquare$