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

1,2

Comments

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

Links

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

David A. Corneth, PARI program

Example

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.

Mathematica

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

Crossrefs

Cf. A000120, A161793.

Sequence in context: A331992 A113570 A065391 * A111261 A276773 A294441

Adjacent sequences: A161789 A161790 A161791 * A161793 A161794 A161795

Keyword

base,nonn

Author

Leroy Quet, Jun 19 2009

Extensions

More terms from Sean A. Irvine, Nov 29 2009

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

Status

approved