BIU numbers (or Sumdivized numbers)
Jelly, 16 15 bytes

ÆDÆfQ€SS‘ḍ
1Ç#Ṫ


Try it online!

Woohoo for builtins (but they mysteriously hide from me sometimes so -1 byte thanks to @HyperNeutrino)

How it Works

ÆDÆfQ€SS‘ḍ - define helper function: is input a BIU number?
ÆD             - divisors
  Æf           - list of prime factors
    Q€         - now distinct prime factors
      SS       - sum, then sum again ('' counts as 0)
        ‘      - add one (to account for '')
         ḍ     - does this divide the input?

1Ç#Ṫ - main link, input n
  #     - starting at 
1          - 1
        - get the first n integers which meet:
 Ç         - helper link
   Ṫ    - tail