

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.


0




OFFSET

1,2


COMMENTS

In binary:
 the product of numbers of 0's and 1's for an Ndigit number is at most N^2/4,
 the least Ndigit number is 2^(N1),
 for N >= 11, (N^2/4)^2 < 2^(N1).
Hence there are no terms >= 2^10.
(End)


LINKS



FORMULA



EXAMPLE

625 > 1001110001; five '0' and five '1'; 5*5=25; sqrt(625)=25.
324 > 101000100; 3 '0' and 6 '1'; 3*6=18; sqrt(324)=18.


MATHEMATICA

Select[Range[8! ], DigitCount[ #, 2, 0]*DigitCount[ #, 2, 1]==Sqrt[ # ]&]


PROG

(PARI) isok(n) = {n1 = hammingweight(n); n0 = #binary(n)  n1; (n0*n1)^2 == n; } \\ Michel Marcus, Nov 19 2015


CROSSREFS



KEYWORD

nonn,base,full,fini


AUTHOR



EXTENSIONS



STATUS

approved



