Hard to tell, it depends on if that is the engine production code or the car/engine serial number. It can be decoded two ways depending on which number it is.
Assuming it is the car/engine serial number, it decodes like this:
4 = Series 4400/LeSabre
I = 1962
1 = Flint, MI
060571 = sequential number, range for Flint built fullsize cars was 001001 to 101495
Assuming it is the engine production code number, it decodes like this:
4I = 401 V8 w/ 4-bbl carb and 10.25:1 compression ratio (Wildcat 445)
1060571 = sequential engine number
My guess is that the number you provided is the car/engine serial number and not the engine production code number because the sequential engine serial number would be too high compared to the total production.
1962 is a tricky year, if you have pictures of both the engine production code and the engine serial number that would be helpful. The engine production code is located on the passenger side of the engine in front of the valley cover and the engine serial number is located on the driver side of the engine in front of the valley cover. In 1963 Buick changed the engine production code scheme so it was not possible to confuse the engine production code and the engine serial number like you can in 1962.
Buickman Award 2015
1957 Special 4-door Riviera (hardtop) model 43