I thought they had one that used an A?
There was a tractor with an A engine , but it was officially called the Handiman Jr. Basically it was the rebirth of the 1933 model, which would have had either an I or a K engine. This Jr model came out in the 1935 catalog first. The fuel tanks on the 33 and Jr models were mounted on a separate bracket behind the engine. For 1937 you could have bought a model Z37, C37,or B37, each with 4,3 or 2hp. The A37 is the Handiman Jr rehashed.
Lots of strange stuff in the early tractors, as at one time the tractor was called a Bradley Handiman, instead of Sears. You were offered basic models and it appears that you could alter them with larger wheels, and different engine sizes. In the 1935 catalog I have, it says you could get a heavy duty engine with more power, but don't say what that engine is. I also noticed that in the early days the tractors were shipped from Philly or Boston, instead of the Bradley factory named later. I saw a paper one time, that showed where Briggs built the gear cases for the 1933 model, so I don't know if that meant they built the whole tractor at one of there plants, or just the trannys and engines.