Trouble pairing a Logitech K380 bluetooth keyboard with AppleTV 4. Any suggestions?

Bought a Logitech K380 bluetooth keyboard to use with my AppleTV 4. So far I have had no trouble pairing other devices including several pairs of headphones. The keyboard pairs fine with my iPad running iOS 9. It just doesn't pair with the AppleTV. I go to bluetooth in the AppleTV 4 in the settings and turn on pairing on the keyboard, but it never shows up as a discoverable device. I've restarted the AppleTV, the keyboard, and tried a few things. So far, nothing. Any suggestions?