Divisor Sum of 6368

Example of Divisor Sum of Integer

$\map {\sigma_1} {6368} = 12 \, 600$

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:

$6368 = 2^5 \times 199$

Hence:

$\ds \map {\sigma_1} {6368}$

$=$

$\ds \frac {2^6 - 1} {2 - 1} \times \paren {199 + 1}$

$\ds $

$=$

$\ds \frac {63} 1 \times 200$

$\ds $

$=$

$\ds \paren {3^2 \times 7} \times \paren {2^3 \times 5^2}$

$\ds $

$=$

$\ds 2^3 \times 3^2 \times 5^2 \times 7$

$\ds $

$=$

$\ds 12 \, 600$

$\blacksquare$