Buszko, writing in the Encyclopedia of the Holocaust, explains why some prisoners were tattooed, while others were not:
Prisoners were registered and received numbers tattooed on their left arm upon leaving the quarantine in Birkenau for forced labor in Auschwitz or in one of the subcamps. The same procedure applied to those prisoners who were directed straight to Auschwitz I: 405,000 prisoners were registered in this way.
[Ed. Note: Buszko later notes that only 65,000 of those so registered and tattooed survived. knm]
Not included in any form of registration were the vast majority of the Auschwitz victims, those men and women who, upon arrival in Auschwitz II, were led to the gas chambers and killed there immediately. Also not included in the registration were those prisoners who were sent to work in other concentration camps not belonging to the Auschwitz system. ... Still another group of unregistered prisoners were those who were designated for execution after a short stay in the camp. That group consisted mainly of hostages, Soviet army officers, and partisans. (Encyclopedia, Vol. I, 110-111)