You can easly find the HP product number of any of your HP server by looking on the server itself or on the warranty card.
The HP product number is nice to have if you want to easily find that date your HP server will be out of warranty.
This product number is no longer mandatory if you are using this Warranty check tool, but in some case you will still need it.
If your HP server was built using HP SmartStart the product number could be found in the windows registry:
HKLM\HARDWARE\DESCRIPTION\System\BIOS\SystemSKU
Here is how to use powershell to read this information:
$reg = [Microsoft.Win32.RegistryKey]::OpenRemoteBaseKey('LocalMachine', "NameOfServer")
$regkey = $reg.OpenSubkey("HARDWARE\\DESCRIPTION\\System\\BIOS")
$SystemSku = $regkey.GetValue("SystemSku")