Jelly, 8 bytes
1DS=ÆdƲ# Takes \$n\$ on STDIN, and outputs the first \$n\$ values.
How it works
1DS=ÆdƲ# - Main link. Takes no arguments Ʋ - Group the previous 4 links into a monad f(k): D - Digits of k S - Sum Æd - Divisor count of k = - Are they equal? 1 # - Read n from STDIN and find the first n k≥1 such that f(k) is true