The complete list of n for which Q(ζn) has unique factorization is 1 through 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 40, 42, 44, 45, 48, 50, 54, 60, 66, 70, 84, 90.

Source; https://en.wikipedia.org/wiki/Cyclotomic_field#List_of_class_numbers_of_cyclotomic_fields

The complete list of $n$ for which ${\bf Q}(\zeta_n)$ has unique factorization is 1 through 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 40, 42, 44, 45, 48, 50, 54, 60, 66, 70, 84, 90.

Source; https://en.wikipedia.org/wiki/Cyclotomic_field#List_of_class_numbers_of_cyclotomic_fields