This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A386372 #19 Jul 22 2025 10:33:17
%S A386372 1,9,729,4782969,14348907,19073486328125,363797880709171295166015625
%N A386372 Odd numbers of the form k^m that have m binary digits 1.
%C A386372 5^89 is a term.
%H A386372 David A. Corneth, <a href="/A386372/a386372.gp.txt">PARI program</a>
%e A386372 9 = 3^2 = 1001_2 is in the sequence since it is a second power and it has two binary digits 1.
%e A386372 729 = 3^6 = 1011011001_2 is in the sequence since it is a sixth power and it has six binary digits 1.
%t A386372 With[{nn = 2^30}, {1}~Join~Select[Union@ Flatten@ Table[a^2*b^3, {b, Surd[nn, 3]}, {a, Sqrt[nn/b^3]}], And[OddQ[#], 1 < #2 == DigitCount[#1, 2, 1]] & @@ {#, GCD @@ FactorInteger[#][[;; , -1]]} &] ] (* _Michael De Vlieger_, Jul 21 2025 *)
%o A386372 (PARI) \\ See Corneth link
%Y A386372 Cf. A000120, A001597, A075109, A161792.
%K A386372 nonn,base,more
%O A386372 1,2
%A A386372 _David A. Corneth_, Jul 19 2025