A161792 If b(m) is the number of 1's in the binary representation of m, then the positive integer m is included if m = k^b(m), for some integer k.

1, 2, 4, 8, 9, 16, 32, 36, 64, 128, 144, 256, 512, 576, 729, 1024, 2048, 2304, 4096, 8192, 9216, 16384, 32768, 36864, 46656, 65536, 131072, 147456, 262144, 524288, 589824, 1048576, 2097152, 2359296, 2985984, 4194304, 4782969, 8388608, 9437184, 14348907, 16777216

Offset: 1

Author

Leroy Quet, Jun 19 2009

Keywords

• base
• nonn

Comments

Contains every power of 2. - Sean A. Irvine, Nov 29 2009

Examples

			36 in binary is 100100, which has two 1's. Since 36 = 6^2, with an exponent of 2, then 36 is included in this sequence.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..275 (terms <= 2^150)
• David A. Corneth, PARI program

Crossrefs

Cf. A000120, A161793.

Programs

Mathematica

q[m_] := IntegerQ[Surd[m, DigitSum[m, 2]]]; Select[Range[10^5], q] (* Amiram Eldar, Jul 19 2025 *)

Extensions

More terms from Sean A. Irvine, Nov 29 2009

a(40)-a(41) from Amiram Eldar, Jul 19 2025