I think this is some type of Gymnocactus. And to use a Garden Web term, itÂs also pup-iferous.
According to flower and spines it seems to be Gymnocactus knuthianus. Though it surprises me that it is offsetting.
Looks like Knuthianus to me too, (now Turbinicarpus knuthianus thanks to the lumpers), according to Backeberg's lexicon the species sometimes offsets (becoming puppiferous).