Solaris and IRIX don't have a 'screen' terminfo entry by default, so you might notice that if you set TERM to 'screen' things don't work right. This is especially true when you want to use terminal multiplexers like screen or tmux.

Screen itself comes with a termcap entry. If you install using the sunfreeware package, the termcap file will be: /usr/local/doc/screen/terminfo/screencap.
Otherwise, you can download this one.

We need to convert this to a terminfo file and compile it. All tools used below come standard with Solaris / IRIX.

$ captoinfo screencap > screen.ti
"screencap", line 2, col 24, terminal 'screen': unknown capability 'G0'
"screencap", line 18, col 58, terminal 'screen': unknown capability 'AX'
$ sudo tic screen.ti
$ ls -d /usr/share/lib/terminfo/s/screen*
/usr/share/lib/terminfo/s/screen     /usr/share/lib/terminfo/s/screen-w

Note: Make sure you're running /usr/bin/tic, not /usr/local/bin/tic (comes with some sunfreeware package). The /usr/local/bin/tic will write it's terminfo file to /usr/local/share/terminfo which isn't used by any shell I've tried, not by default anyway. Something to keep in mind.

Now you've got a 'screen' terminfo entry. Setting your TERM to 'screen' should work now, which is the default inside new screen and tmux sessions.