For those who are curious how we can construct such a function, and why it looks so funky on the negative side, I strongly recommend this video https://www.youtube.com/watch?v=v_HeaeUUOnc

I think they mean a (traditionally) closed form expression, for which I don't know if there is a particularly simple explanation of why there isn't such a form but there is for summing integers to n instead of multiplying them.