Triplet in Arithmetic Sequence with equal Divisor Sum

Theorem
The smallest triple of integers in arithmetic sequence which have the same divisor sum is:
 * $\map {\sigma_1} {267} = \map {\sigma_1} {295} = \map {\sigma_1} {323} = 360$

Proof
We have that:

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

Then: