Divisor Sum of 7192

Example of Divisor Sum of Integer

$\map {\sigma_1} {7192} = 14 \, 400$

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:

$7192 = 2^3 \times 29 \times 31$

Hence:

$\ds \map {\sigma_1} {7192}$

$=$

$\ds \frac {2^4 - 1} {2 - 1} \times \paren {29 + 1} \times \paren {31 + 1}$

$\ds $

$=$

$\ds \frac {15} 1 \times 30 \times 32$

$\ds $

$=$

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

$\ds $

$=$

$\ds 2^6 \times 3^2 \times 5^2$

$\ds $

$=$

$\ds 14 \, 400$

$\blacksquare$