a(n) is the least perfect power A001597 with binary weight n.

Terms

a(0) =1a(1) =9a(2) =25a(3) =27a(4) =121a(5) =125a(6) =1521a(7) =2025a(8) =5625a(9) =24025a(10) =42875a(11) =59319a(12) =32761a(13) =393129a(14) =851929a(15) =1540081a(16) =6275025a(17) =15327225a(18) =27258841a(19) =41925625a(20) =127893481a(21) =243204025a(22) =385611769a(23) =268336125a(24) =1979449081a(25) =4823441401a(26) =12870221809a(27) =25698491351a(28) =51354402813a(29) =127506840561