There are two generations of the Takumar 105/2.8. The first generation consists of 4 elements in 4 groups and the second generation (and also the Pentax 105/2.8) consists of 5 elements in 4 groups (with the rear two elements cemented).
This is a lens from 1959-1961 (or, maybe, 1959-1963). As far as I know, earlier versions were marked as "1:2.8 f=105mm", so this one ("1:2.8/105") is later.
The Auto-Takumar 105/2.8 is optically the same as the Takumar 105/2.8 (Pre-Set I):
So its optical design is 4 elements in 4 groups (without cemented elements).
The filter thread size is 49mm (while the Pre-Set Takumar has 46mm).
The aperture has 8 blades.
This lens is called Auto-Takumar because of its special aperture control. Under normal conditions, the aperture is controlled directly by the aperture ring (with click stops at f/2.8, f/3.3, f/4, f/4.8, f/5.6, f/6.7, f/8, f/9.5, f/11, f/16, f/22).
However, the aperture mechanism can be manually cocked with the lever on the lens to fully open the aperture (for easier focusing).
During shooting, if the camera supports it, the small (stop-down) pin is pressed to close the aperture to the set value.
Then cock the lens lever again to repeat the cycle.
Despite the name Auto, this is semi-automatic, as opposed to the later fully automatic aperture control lenses called Super-Takumars and so on.
This semi-automatic aperture control is completely useless in modern use with an M42x1 adapter. If an adapter keeps the small pin pressed, it is impossible to cock the lever. If an adapter doesn't push the small pin, you can cock the lever, but the lens should be removed to manually push the small pin to close the aperture. So the only way is to control the aperture directly with the ring without using the lever. Of course, the pre-set versions (both generations) are much more convenient to use with an adapter.
So, now I have two generations of the Takumar 105/2.8:
(The Auto-Takumar and the Pre-Set Takumar)
And I can compare 4/4 and 5/4 optical designs of 105/2.8!