Gran Turismo series LTD as September 2017: 77.02M (sell-in)There is mixed messaging in regard to this factoid. Kaz's tweet seems to say total player count yet the official GT account seems to imply that it's just referring to the players who participated in the GT Championship.
Gran Turismo series LTD as May 5, 2018: 80.40M (sell-through)
So at least it's safe to say GTS sold more than 3.38M for now.
Sources:
https://web.archive.org/web/20180226220432/www.polyphony.co.jp/products/
http://www.polyphony.co.jp/products/