What is my 'apple account number?'

Do you mean the serial number for the iPod > iPod: How to find the serial number

Not sure what you mean by "apple account number" unless you are referring to your Apple ID which is required > iPod nano Replacement Program

I think the O.P might be refering to the account phone number. Apple just never quite seems to fully get the message that an old phone number connected to an Apple ID isn't desirable.