Isn't the core showing up in your console? If so, just right-click the core and select Inventory Scan like you would any other workstation.
If you want to run a manual scan:
"C:\Program Files\LANDesk\LDClient\LDISCN32.EXE" /NTT=LANDESK:5007 /S=LANDESK /I=HTTP://LANDESK/ldlogon/ldappl3.ldz /V /SYNC
Replace LANDESK at the 3 places in the command-line with your server name.
As well as running the command listed, FYI, the Core runs an inventory scan on itself each night during its maintenance routine so you should see the data updated the following day. It does this without the need for an agent installation on the core.
Mark Star - MarXtar LANDesk Enhancements
Home of Power State Notifier & Wake-On-WAN for LANDesk