A099771 Smallest n-aspiring number. That is, a(n) = smallest k such that s^(n)(k) is perfect but s^(n-1)(k) is not, where s(k) is the sum of the aliquot parts of k and s^(i) means iterate s i times.

25, 95, 417, 675, 2541, 3888, 3528, 16256, 13984, 11312, 10648, 10688, 6672, 15364, 20476, 12288, 12636, 32216, 33304, 33896, 34504, 38660, 31824, 15792, 62296, 67304, 49120, 58104, 102740, 82120, 84704, 53680