If you want to know exactly what the Mix Color mode "Color" does, here is a mathematical explanation:

The color A gets scaled by 1 - Factor. Then a combination of color B's Hue and Saturation with color A's Value will be scaled by the Factor. The results of these scalings/multiplications are added together to give the final result.

So this setup:

can be recreated mathematically with this node setup (well, actually you can do it with less nodes, I just extended it a bit to show the components a bit better):

If you want to know exactly what the Mix Color mode "Color" does, here is a mathematical explanation:

The color A gets scaled by 1 - Factor. A combination of color B's Hue and Saturation with color A's Value will be scaled by the Factor. The results of these scalings/multiplications are added together to give the final result.

So this setup:

can be recreated mathematically with this node setup (well, actually you can do it with less nodes, I just extended it a bit to show the components a bit better):