The 360/20.
It's seems unlike to me that it was really the inspiration for
the minicomputer families. They had already build minicomputer-class
machines in the past (e.g., 650, 1401, 1620/1710), and were fairly
successful with them.
Maybe not an inspiration, but certainly a rebirth. S/360 was supposed to
do all the jobs for business (not counting process control or lab use).
Don't you remember the 360 slogan: It Runs The "Full Circle" of
Applications!
(get it? 360, Full Circle...well, not as clever as IBM's "CADET"
machine...)
-Mike Cheponis