I have two Logitech K400R wireless keyboards. Let's call them Fred and Barney. They're great. Each has a tiny USB thingy - dongle makes me think there's some kind of wire. It's just a tiny little thing that plugs into USB. Turns out it's a Unifying Receiver. I'll come back to that.
In my case, I'm only able to put my hands on Keyboard Fred and Receiver Barney. The other keyboard and the other receiver are probably on vacation somewhere. So I've got this mismatched set. Plugged in the receiver and turned on the keyboard and... nothing.
Well I googled and discovered there's software for the Unifying Receiver. Don't know how that could possibly solve my problem, but I download and install it.
(You'll find it here: https://www.logitech.com/en-us/manuals/11916)
To make a longish story shorter, when you plug in the Unifying Receiver (oh and it might even be from yet another Logitech device) and turn on the K400R, it will detect that keyboard and set up a connection. My mismatched Fred Keyboard and Barney Receiver are working great!
Thanks, Logitech!!