Divisor Sum of 17,296

Example of Divisor Sum of Integer

$\map {\sigma_1} {17 \, 296} = 35 \, 712$

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:

$17 \, 296 = 2^4 \times 23 \times 47$

Hence:

$\ds \map {\sigma_1} {17 \, 296}$

$=$

$\ds \frac {2^5 - 1} {2 - 1} \times \paren {23 + 1} \times \paren {47 + 1}$

$\ds $

$=$

$\ds \frac {31} 1 \times 24 \times 48$

$\ds $

$=$

$\ds 31 \times \paren {2^3 \times 3} \times \paren {2^4 \times 3}$

$\ds $

$=$

$\ds 2^7 \times 3^2 \times 31$

$\ds $

$=$

$\ds 35 \, 712$

$\blacksquare$