I havent really considered this a core of my team until i was reading this thread lol, but in retrospect it does function very well as the core of one of my teams:
Jirachi@Leftovers
Serene Grace|Careful: 236HP/20ATK/252SDef
Moves: Stealth Rock/Thunder Wave/Iron Head/Fire Punch
Latios@ Life Orb
Levitate|Timid: 4HP/252SAtk/252Spe
IVs:31/30/31/30/31/30
Moves: Draco Meteor/Surf/Psyshock/HP [Fire]
Slowbro @ Leftovers
Regenerator| Bold: 252HP/252Def/4SAtk
Moves: Slackoff/Scald/Flamethrower/Toxic
This group synergizes (idek if thats a word) well enough together that I find that they are always the "last half" if a battle is going down hill for me. Its not that the other 3 members are expendable, its just that these three work so well together that it increases their longevity. Jirachi trolls with the moveset and sets uf the much needed stealth rock for latios (then again its OU so what is OU w/o rocks?). when some poke comes to threaten out rachi (whether it be some ground or fire move) then latios comes in to halt the ground and take the fire, with slowbro having the same ability. Latios has moves that hit 10/17 types super effective, and has perfect coverage on neutral damage. But if some other dragon type has come in, either rachi or bro come in to take the special or physical dragon move, respectively. And coupled with SR, they can then cripple the opposing dragon with either twave or toxic, effectively aiding Latios' sweeping powers. Only problems are the all linear weakness to ghost and dark, but the others on the team take care of that problem.