It can produce outputs that resemble calculations.
It can prompt an agent to input some numbers into a separate program that will do calculations for it and then return them as a prompt.
Neither of these are calculations.
Edit: the implication comes from demanding that the OP’s definition must be rigorous enough to cover all models of “computation”, and by failing to do so, it means that LLMs must be more like humans than computers.
You are wrong. Especially that we are talking about models with 50T parameters.
Can they do arbitrary computations for arbitrarily long numbers? Nope. But that's not remotely the same statement, and they can trivially call out to tools to do that in those cases.
I think there are differences, and I think we can make good guesses, but I'm not sure we can reliably classify a P-zombie from a normal human from their behaviour with 100% accuracy..