so to say that you have a coin which can competatively mined with even weak cpus ? enabling to use old smartphones or old laptops as miners, to put these old devices to a use?
It's hard to imagine that this is possible. If it actually is PoW then stronger CPUs would be able to do the work faster than weaker CPUs which would make mining with weak CPUs less profitable.
Also if you have a fixed mining puzzle it is always possible to build circuits that are solely made to solve this particular puzzle (a.k.a ASICs). One possibility to circumvent this might be to use a mining puzzle that is not fixed but changes from time to time, pretty much like the difficulty of crypto currencies is always changing. I don't really know if and how you could implement this in a way that makes sense but it might be possible. This would make ASICs useless because you would need some kind of general computing machine to mine such a coin.
It would also be possible to create a mining puzzle which does not require you to provide computing power but a different resource instead. For example storage. But this would not be PoW of course.