OFFSET
1,2
COMMENTS
No other terms of the form 3^m or 5^m for m <= 10^6. - Michael S. Branicky, Sep 27 2025
LINKS
David A. Corneth, PARI program
EXAMPLE
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.
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 *)
PROG
(PARI) \\ See Corneth link
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
David A. Corneth, Jul 19 2025
EXTENSIONS
a(8) from Zhao Hui Du, Sep 26 2025
STATUS
approved