A386242 a(n) is the least perfect power A001597 with binary weight n.

1, 9, 25, 27, 121, 125, 1521, 2025, 5625, 24025, 42875, 59319, 32761, 393129, 851929, 1540081, 6275025, 15327225, 27258841, 41925625, 127893481, 243204025, 385611769, 268336125, 1979449081, 4823441401, 12870221809, 25698491351, 51354402813, 127506840561, 205822820329

Offset: 1

Author

Hugo Pfoertner, Jul 23 2025

Keywords

• nonn
• base

Crossrefs

Cf. A000120, A001597, A231897.

Programs

Mathematica

upto = 10^11; L = Table[2 upto, {2 + Log2@ upto}]; Do[n = 1; While[(v = n^k) <= upto, nb = Plus @@ IntegerDigits[v, 2]; If[L[[nb]] > v, L[[nb]] = v]; n++], {k, 2, Log2[upto]}]; Take[L, Position[L, 2 upto][[1, 1]] - 1] (* Giovanni Resta, Jul 23 2025 *)

Extensions

a(27)-a(31) from Giovanni Resta, Jul 23 2025