@Rostrum, Welcome to HP Support Community!
If you have a Deskjet 3630, Deskjet 3700, or Deskjet 2600 printer, you can only produce the claim code by printing the page. If only one cartridge is empty, remove it and try to print the page with the remaining cartridge.
I'd suggest you buy at least one cartridge to enroll in the program after which ink will be supplied by HP.
Refer to the document HP Printers - Having Trouble Claiming Your Printer? for help.
I hope that answers your concern adequately. Let me know!
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TEJ1602
I am an HP Employee