Triplet in Arithmetic Sequence with equal Sigma

Theorem

The smallest triple of integers in arithmetic sequence which have the same $\sigma$ (sigma) value is:

$\map \sigma {267} = \map \sigma {295} = \map \sigma {323} = 360$

Proof

We have that:

 $\ds 295 - 267$ $=$ $\ds 28$ $\ds 323 - 295$ $=$ $\ds 28$

demonstrating that $267, 295, 323$ are in arithmetic sequence with common difference $28$.

Then:

 $\ds \map \sigma {267}$ $=$ $\ds 360$ $\sigma$ of $267$ $\ds \map \sigma {295}$ $=$ $\ds 360$ $\sigma$ of $295$ $\ds \map \sigma {323}$ $=$ $\ds 360$ $\sigma$ of $323$