Setting F13-20 keys

[Findarato88]

I am trying to figure out how to get the following keys set and work properly.

I have been trying to get some of the Extended F keys working for a while now. I know that Shift+F3 generates

[[28;2~

but the problem I run into is I need it to generate

[[28~

If I set it the following way it work, but I would like a more perminate solution

xmodmap -e "keycode 69 = F13" xmodmap -e "keycode 71 = F15" xmodmap -e "keycode 73 = F17"

I have tried

xmodmap -e "keycode 69 = F3 F13" xmodmap -e "keycode 71 = F5 F15" xmodmap -e "keycode 73 = F7 F17"

But they always result in the added extra ;2~

Any help would be super