Divisor Sum of 1210
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {1210} = 2394$
where $\sigma_1$ denotes the divisor sum function.
Proof
- $\ds \map {\sigma_1} n = \prod_{1 \mathop \le i \mathop \le r} \frac {p_i^{k_i + 1} - 1} {p_i - 1}$
where $n = \ds \prod_{1 \mathop \le i \mathop \le r} p_i^{k_i}$ denotes the prime decomposition of $n$.
We have that:
- $1210 = 2 \times 5 \times 11^2$
Hence:
\(\ds \map {\sigma_1} {1210}\) | \(=\) | \(\ds \paren {2 + 1} \times \paren {5 + 1} \times \frac {11^3 - 1} {11 - 1}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times 6 \times \frac {1330} {10}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times 6 \times 133\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times \paren {2 \times 3} \times \paren {7 \times 19}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2 \times 3^2 \times 7 \times 19\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2394\) |
$\blacksquare$