An apparatus for separating air by cryogenic distillation using a column system comprising a higher pressure column operating at a first pressure and a lower pressure column operating at a second pressure lower than the first pressure, the top of the higher pressure column being thermally coupled to the bottom of the lower pressure column, a first adsorption unit, a second adsorption unit, means for sending a first air flow constituting between 75% and 98% of the air sent to the column system, compressed to a third pressure above the first pressure, to cooling means and then, at the third pressure, to the first adsorption unit in order to be purified of water and of carbon dioxide and means for sending the whole of the purified first flow to the higher pressure column and optionally to the lower pressure column, means for sending a second air flow constituting between 2% and 25% of the air sent to the column system, compressed to a fourth pressure between 1.2 and 2 bar abs and above the second pressure but lower than the third pressure, at the fourth pressure, to the second adsorption unit in order to be purified of water and of carbon dioxide and means for sending the whole of the purified second flow to the lower pressure column, the higher pressure column comprising heat and mass exchange means in order to separate the air to form an oxygen-enriched liquid and a nitrogen-enriched gas, means for sending oxygen-enriched liquid and nitrogen-enriched liquid from the higher pressure column to the lower pressure column, means for drawing off a liquid with a purity of greater than 99%, preferably 99.5% of oxygen from the column system, a pump for pressurizing this liquid, means for vaporizing the pressurized liquid by heat exchange with at least one portion of the first air flow and means for sending an argon-enriched gas from the lower pressure column to the third column and means for drawing off an argon-rich fluid at the top of the third column.