Weird Number/Examples/836

Example of a Weird Number
$836$ is a weird number:

The aliquot sum of $836$ is $844$, but no subset of its aliquot parts add to $836$.

Proof
From :
 * $\map \sigma {836} = 1680$

where $\map \sigma {836}$ denotes the $\sigma$ function.

The aliquot sum of $836$ is given by:
 * $\map \sigma {836} - 836 = 1680 - 836 = 844$

The aliquot parts of $836$ are found in :
 * $1, 2, 4, 11, 19, 22, 38, 44, 76, 209, 418$

Note that $8$ is not an aliquot part of $836$, and cannot be made from the aliquot parts of $836$.

Thus $836 = 844 - 8$ cannot be made by any combination of those aliquot parts.

Hence the result.