Sulcorebutia mentosa

This is one of the larger headed species, solitary or clustering when the main head is about 5-7 cm in diameter and producing a patch over time. It distinguishes for the tubercles with chinned bases.
Flowers: Showy that cluster around the lower stem, funnel-shaped with short necks, about 3 cm tall, 3,5 cm in diameter, deep purple or magenta.
Blooming season: Spring.

Some of the information in this description has been found at desert-tropicals.com, llifle.com and cactus-art.biz