Originally posted by Cee Cee it can't be a M or K series, its mounted on a spotmatic which is M42 thread mount. My Guess is a Vivitar or Tamron adaptall type mount ( I think I can see the mount release lever at the rear of the lens right hand side as we look at it) also I think it has 2 sets of F stop numbers one in each direction to suit other brands of cameras who require there fstop numbers to go the other way. I don't recognise the lens but I have a Vivitar 300m 5.5 with a similar adapter on it. (T mount)
the double F stops are the DOF indicator.
In looking again at it, my first impression was wrong, the rubber coated focus ring of a late SMC tak has different dimples, and a second silver ring below them.
also the wide DOF scale indicates this is a wider lens possibly than a 55mm. Perhaps a 35 0r 28 but note, the photo seems to go down to F2 which would make this a really fast wide angle if it is.