The ring of differential operators on a cuspidal curve whose coordinate ring is a numerical semigroup algebra is shown to be a cocommutative and cocomplete left Hopf algebroid. If the semigroup is symmetric so that the curve is Gorenstein, it is a full Hopf algebroid (admits an antipode). Based on joint work with Myriam Mahaman (talk part of the activity of the MIUR Excellence Department Project MATH@TOV CUP CUP E83C23000330006).