A386372 Odd numbers of the form k^m that have m binary digits 1.

1, 9, 729, 4782969, 14348907, 19073486328125, 363797880709171295166015625

Offset: 1

Author

David A. Corneth, Jul 19 2025

Keywords

• nonn
• base
• more

Comments

5^89 is a term.

Examples

			9 = 3^2 = 1001_2 is in the sequence since it is a second power and it has two binary digits 1.
729 = 3^6 = 1011011001_2 is in the sequence since it is a sixth power and it has six binary digits 1.
		

Links

• David A. Corneth, PARI program

Crossrefs

Cf. A000120, A001597, A075109, A161792.

Programs

Mathematica

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 *)

PARI

\\ See Corneth link