My printer (hp oj250 mobile) requires hplip 3.16.8, but 3.16.3 is what I got when I installed hplip-gui on my freshly installed 16.04 box.
This is the response from the commands given in the comments to fix the dependencies:
$ sudo apt update&&sudo apt upgrade
[sudo] password for user:
Hit:1 http://ppa.launchpad.net/deluge-team/ppa/ubuntu xenial InRelease
Hit:2 http://archive.ubuntu.com/ubuntu xenial InRelease
Get:3 http://archive.ubuntu.com/ubuntu xenial-security InRelease [102 kB]
Ign:4 http://www.openprinting.org/download/printdriver/debian lsb3.2 InRelease
Hit:5 http://www.openprinting.org/download/printdriver/debian lsb3.2 Release
Fetched 102 kB in 2s (46.4 kB/s)
Reading package lists... Done
Building dependency tree
Reading state information... Done
All packages are up to date.
W: http://www.openprinting.org/download/printdriver/debian/dists/lsb3.2/Release.gpg: Signature by key F8897B6F00075648E248B7EC24CBF5474CFD1E2F uses weak digest algorithm (SHA1)
Reading package lists... Done
Building dependency tree
Reading state information... Done
Calculating upgrade... Done
The following packages were automatically installed and are no longer required:
linux-headers-4.10.0-28 linux-headers-4.10.0-28-generic
linux-image-4.10.0-28-generic linux-image-extra-4.10.0-28-generic
Use 'sudo apt autoremove' to remove them.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
$ sudo apt install -f
Reading package lists... Done
Building dependency tree
Reading state information... Done
The following packages were automatically installed and are no longer required:
linux-headers-4.10.0-28 linux-headers-4.10.0-28-generic
linux-image-4.10.0-28-generic linux-image-extra-4.10.0-28-generic
Use 'sudo apt autoremove' to remove them.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.