# Divisor Sum of 2520

## Example of Divisor Sum of Integer

$\map {\sigma_1} {2520} = 9360$

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:

$2520 = 2^3 \times 3^2 \times 5 \times 7$

Hence:

 $\ds \map {\sigma_1} {2520}$ $=$ $\ds \frac {2^4 - 1} {2 - 1} \times \frac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {7 + 1}$ $\ds$ $=$ $\ds \frac {15} 1 \times \frac {26} 2 \times 6 \times 8$ $\ds$ $=$ $\ds \paren {3 \times 5} \times 13 \times \paren {2 \times 3} \times 2^3$ $\ds$ $=$ $\ds 2^4 \times 3^2 \times 5 \times 13$ $\ds$ $=$ $\ds 9360$

$\blacksquare$