Pyridopyrimidine carboxamide compounds of Formula I are inhibitors of HIV integrase and inhibitors of HIV replication: wherein R1, R2, R3, R4, R5 and R6 are defined herein. The compounds are useful for the prophylaxis or treatment of infection by HIV and the prophylaxis, treatment, or delay in the onset of AIDS. The compounds are employed against HIV infection and AIDS as compounds per se or in the form of pharmaceutically acceptable salts. The compounds and their salts can be employed as ingredients in pharmaceutical compositions, optionally in combination with other antivirals, immunomodulators, antibiotics or vaccines.