This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A173346 #16 Sep 21 2021 21:31:08
%S A173346 0,4,16,144,324,625
%N A173346 Numbers such that the product of numbers of 0's and 1's in the binary representation is equal to the square root of the number.
%C A173346 From _Rémy Sigrist_, Apr 30 2017: (Start)
%C A173346 In binary:
%C A173346 - the product of numbers of 0's and 1's for an N-digit number is at most N^2/4,
%C A173346 - the least N-digit number is 2^(N-1),
%C A173346 - for N >= 11, (N^2/4)^2 < 2^(N-1).
%C A173346 Hence there are no terms >= 2^10.
%C A173346 (End)
%F A173346 Terms satisfy m = A071295(m)^2. - _Michel Marcus_, Nov 19 2015
%e A173346 625 -> 1001110001; five '0' and five '1'; 5*5=25; sqrt(625)=25.
%e A173346 324 -> 101000100; 3 '0' and 6 '1'; 3*6=18; sqrt(324)=18.
%t A173346 Select[Range[8! ],DigitCount[ #,2,0]*DigitCount[ #,2,1]==Sqrt[ # ]&]
%o A173346 (PARI) isok(n) = {n1 = hammingweight(n); n0 = #binary(n) - n1; (n0*n1)^2 == n;} \\ _Michel Marcus_, Nov 19 2015
%Y A173346 Cf. A071295.
%K A173346 nonn,base,full,fini
%O A173346 1,2
%A A173346 _Vladimir Joseph Stephan Orlovsky_, Feb 16 2010
%E A173346 Minor edits by _N. J. A. Sloane_, Feb 21 2010
%E A173346 a(1) = 0 inserted by _Michel Marcus_, Nov 19 2015