Divisor Sum of 9272

Example of Divisor Sum of Integer

$\map {\sigma_1} {9272} = 18 \, 600$

where $\sigma_1$ denotes the divisor sum function.

$\ds \map {\sigma_1} n = \prod_{1 \mathop \le i \mathop \le r} \frac {p_i^{k_i + 1} - 1} {p_i - 1}$

where $n = \ds \prod_{1 \mathop \le i \mathop \le r} p_i^{k_i}$ denotes the prime decomposition of $n$.

We have that:

$9272 = 2^3 \times 19 \times 61$

Hence:

$\ds \map {\sigma_1} {9272}$

$=$

$\ds \frac {2^4 - 1} {2 - 1} \times \paren {19 + 1} \times \paren {61 + 1}$

$\ds $

$=$

$\ds \frac {15} 1 \times 20 \times 62$

$\ds $

$=$

$\ds \paren {3 \times 5} \times \paren {2^2 \times 5} \times \paren {2 \times 31}$

$\ds $

$=$

$\ds 2^3 \times 3 \times 5^2 \times 31$

$\ds $

$=$

$\ds 18 \, 600$

$\blacksquare$