# Sigma Function of Integer/Examples

## Examples of $\sigma$ Function of Integer

Let $\sigma: \Z_{>0} \to \Z_{>0}$ denote the $\sigma$ function: the sum of all the positive integer divisors of $n$.

### $\sigma$ of $1$

$\map \sigma 1 = 1$

### $\sigma$ of $3$

$\sigma \left({3}\right) = 4$

### $\sigma$ of $12$

$\sigma \left({12}\right) = 28$

### $\sigma$ of $20$

$\sigma \left({20}\right) = 42$

### $\sigma$ of $24$

$\sigma \left({24}\right) = 60$

### $\sigma$ of $40$

$\sigma \left({40}\right) = 90$

### $\sigma$ of $44$

$\map \sigma {44} = 84$

### $\sigma$ of $48$

$\sigma \left({48}\right) = 124$

### $\sigma$ of $207$

$\sigma \left({207}\right) = 312$

### $\sigma$ of $12 \, 496$

$\sigma \left({12 \, 496}\right) = 26 \, 784$

### $\sigma$ of $14 \, 288$

$\sigma \left({14 \, 288}\right) = 29 \, 760$