[math-fun] Cutting a pie to share equally among up to n people

Suppose we want to make cuts in a circular pie (the usual kind of cut, from the center to a point on the perimeter) in such a way that, for every k between 1 and n, the pieces can be divided equally among k people, each of whom gets the same amount of pie. How many cuts are needed? (I'm guessing I'm not the first person to ask this question. Searching the OEIS for the words "cut pizza" yielded several hits, none of which were my sequence. Searching the OEIS for the words "cut pie" yielded no hits at all. Not sure what this says about the eating preferences of mathematicians.) Jim Propp