The machine came with Mountain Lion, I believe. I upgraded to Mavericks, Yosemite, El Capitan and Sierra. Went to High Sierra, but reverted back to Sierra. Fortunately, each time I did make a flash pen boot drive BEFORE installing the OS.
UPDATE: If I go to App Store / Store / View My Account in the dropdown menu, I can then HIDE or UNHIDE purchases. Sometime along the way I had chosen to hide some purchases . . . which included all the aforementioned OS downloads. (Emphasis added)
Mystery solved!
All except Sierra and High Sierra, I presume.