a(n) is the first term of the first run of exactly n non-perfect-powers.

Terms

a(0) =26a(1) =2a(2) =5a(3) =28a(4) =0a(5) =10a(6) =97337a(7) =17a(8) =2188a(9) =3126a(10) =2198a(11) =37a(12) =0a(13) =50a(14) =129a(15) =65a(16) =226a(17) =82a(18) =197a(19) =101a(20) =0a(21) =2026a(22) =1001a(23) =145a(24) =42850a(25) =170a(26) =485a(27) =0a(28) =6860a(29) =0