Divisor Sum of Integer/Examples/44

Example of Divisor Sum of Integer

 * $\map {\sigma_1} {44} = 84$

where $\sigma_1$ denotes the $\sigma$ function.

Proof
From Divisor Sum of Integer
 * $\ds \map {\sigma_1} n = \prod_{1 \mathop \le i \mathop \le r} \frac {p_i^{k_i + 1} - 1} {p_i - 1}$

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

We have that:
 * $44 = 2^2 \times 11$

Hence: