In the mathematics of the ancient Greek 1 has not been considered to be a number. Nevertheless 1 counted as a divisor of perfect numbers like 6 = 1 + 2 + 3. Is there any explanation for this inconsistency?
Euclid (and this is not "the Greeks", although the same definition can be found in other places as well) defined a number as a multitude of ones. Since 1 is not a multitude of ones, 1 was not a number. 6, on the other hand, is a multitude of ones, and for this reason has 1 as a divisor. And since 6 is not a multiple of 6, its only divisors were 1, 2 and 3. In particular, there is no inconsistency whatsoever in your example.
Occasionally Euclid includes 1 as a number, in particular in a couple of propositions that are believed to go back to the Pythagoreans.
I am not convinced that there is any inconsistency. In El. VII, def. 2 Euclid writes “A number is a multitude composed of units.” ( ̓Αριθμὸς δὲ τὸ ἐκ μονάδων συγκείμενον πλῆθος.) In Def. 22 he says: “A perfect number is that which is equal to its own parts.” (Τέλειος ἀριθμός ἐστιν ὁ τοῖς ἑαυτοῦ μέρεσιν ἴσος ὤν.) He does not say that the “parts” of perfect numbers are themselves “numbers”. The parts are a “unit” (that is: 1) and one or more “numbers”.