Were Roman emperors officially considered kings of Egypt?

Question

On this statue of Augustus (image is from Wikipedia), he is depicted wearing the traditional dress of Egyptian pharaohs:

I wonder whether Roman emperors were officially declared kings of Egypt or not, and if yes, who of them was and who was not?

Answer 1

No, they were not. The Ptolemys were the last dynasty to rule Egypt directly in the old fashion. When the Romans took over, they just treated it as another province in the empire.

In 30 BC, following the death of Cleopatra VII, the Roman Empire declared that Egypt was a province (Aegyptus), and that it was to be governed by a prefect selected by the Emperor from the Equestrian and not a governor from the Senatorial order, to prevent interference by the Roman Senate. The main Roman interest in Egypt was always the reliable delivery of grain to the city of Rome.

The headress is called nemes, and is only worn by Pharaohs, sort of like the symbolic function a crown would have to a European. The statue is simply a way of telling those who can't read that Agustus Ceasar is their ruler. However, the Roman rulers never came to Egypt to carry out the cerimonial functions required of a proper Pharaoh. If you look over the dynastic lists, you'll see that they end in 30 BC with Cleopatra.

Answer 2

In 30 BC Cleopatra, Mark Anthony, and Caesarion (Ptolemy Caesar) famously met their deaths in the aftermath of the Battle of Actium at the dawn of the Roman Empire and the Augustan Age.

Ronald Syme (in The Roman Revolution) provides this account of the Ptolemaic dynasty's demise in Egypt:

The children of Cleopatra presented a more delicate problem [opposite the virtue of clemency]. "A multitude of Caesars is no good thing." That just observation sealed the fate of Ptolemy Caesar, whom many believed son of the Dictator [Julius Caesar]. Alexander Helios and Cleopatra Selene were reserved to walk in a Roman triumph. The boy is not heard of again -- he was probably suppressed. The girl was enlisted as an instrument of Roman imperial policy, being given in marriage to Juba, the prince of the Numidian royal stock who became King of Mauretania.

Such was the fate of Egypt's Queen and her children, crowned kinds and queens. The Roman imperator seized the heritage of the Ptolemies. He claimed, using official language to have added the land to the Empire of the Roman People: he treated Egypt as his own private and dynastic possession and governed it trough a viceroy, jealously excluding Roman senators. The first Prefect of Egypt was C. Cornelius Gallus, a Roman knight.

As you may expect, Syme includes references to primary sources, such as Res Gestae Divi Augusti.