Divisor Sum of Integer/Examples/20

Example of Sigma Function of Integer

 * $\map \sigma {20} = 42$

where $\sigma$ denotes the $\sigma$ function.

Proof
From Sigma Function of Integer:
 * $\ds \map \sigma n = \prod_{1 \mathop \le i \mathop \le r} \frac {p_i^{k_i + 1} - 1} {p_i - 1}$

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

We have that:
 * $20 = 2^2 \times 5$

Hence: