According to the Buffalo Sabres Wikipedia page regarding draft picks, for what it is worth, the Buffalo Sabres have since their inception into the participated in 42 NHL Entry Drafts and 6 supplemental drafts as a member of the National Hockey League.
That amounts to 448 draft picks in the history of the franchise. Buffalo has drafted nineteen players in the history of the franchise that have gone on to play for teams that have won the Stanley Cup. They also have two invalid claims – one that has been stricken from official records, but is a great feel good story for its fans.