Board Thread:Lore Discussion/@comment-177.180.69.165-20130504030355/@comment-7599817-20130504045111

You are good there are 16 total artifacts available on a striaght no mod playthrough. So not getting Hircine's Ring (Skyrim) still allows you to get 15 and the achievement. You just have to do all the other Daedric Quests (Skyrim) to get it.