A084561 Numbers with a square number of 1's in their binary expansion.

0, 1, 2, 4, 8, 15, 16, 23, 27, 29, 30, 32, 39, 43, 45, 46, 51, 53, 54, 57, 58, 60, 64, 71, 75, 77, 78, 83, 85, 86, 89, 90, 92, 99, 101, 102, 105, 106, 108, 113, 114, 116, 120, 128, 135, 139, 141, 142, 147, 149, 150, 153, 154, 156, 163, 165, 166, 169, 170, 172, 177, 178

Offset: 1

Author

Jason Earls, Jun 27 2003

Keywords

• easy
• nonn
• base

Comments

Begins to differ from A084345 at the 22nd term.

There are A003099(n) terms with at most n bits, so a(n) is n sqrt log n times a bounded function of n (which does not tend toward a limit). - Charles R Greathouse IV, Mar 26 2013

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001969, A000069, A052294, A084345.

Programs

Mathematica

Select[Range[0,178],IntegerQ[Sqrt[Count[IntegerDigits[#,2],1]]]&] (* Jayanta Basu, May 24 2013 *)

PARI

is(n)=issquare(hammingweight(n)) \\ Charles R Greathouse IV, Mar 26 2013