Divisor Sum of Integer/Examples/40

Example of Sigma Function of Integer

 * $\map \sigma {40} = 90$

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

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

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

We have that:
 * $40 = 2^3 \times 5$

Hence: