Triplet in Arithmetic Sequence with equal Divisor Sum

Theorem
The smallest triple of integers in arithmetic progression which have the same $\sigma$ (sigma) value is:
 * $\sigma \left({267}\right) = \sigma \left({295}\right) = \sigma \left({323}\right) = 360$

Proof
We have that:

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

Then: