Put the clementines in a pot with cold water to cover, bring to the boil, and cook for 2 hours. Drain and, when cool, cut each clementine in half and remove the seeds. Then finely chop the skins, pith, and fruit in the processor (or by hand, of course).
Preheat the oven to 375 degrees F.
Butter and line an 8-inch springform pan with parchment paper.
Beat the eggs. Add the sugar, almonds, and baking powder. Mix well, adding the chopped clementines. I don't like using the processor for this, and frankly, you can't balk at a little light stirring.
Pour the cake mixture into the prepared pan and bake for 1 hour, when a skewer will come out clean; you'll probably have to cover the cake with foil after about 40 minutes to stop the top from burning. Remove from the oven and leave to cool, in the pan on a rack. When the cake is cold, you can take it out of the pan. I think this is better a day after it's made, but I don't complain about eating it anytime.
I've also made this with an equal weight of oranges and lemons, in which case I increase the sugar to 1 1/4 cups and slightly Anglicize it, too, by adding a glaze made of confectioners' sugar mixed to a paste with lemon juice and a little water.