A117891 Numbers n such that both the number of non-leading 0's in the binary representation of n and the number of 1's in the binary representation of n divide n.

2, 4, 6, 10, 12, 16, 18, 24, 36, 40, 42, 48, 55, 60, 80, 84, 108, 110, 120, 126, 132, 144, 156, 172, 180, 184, 192, 204, 212, 216, 222, 228, 232, 240, 246, 252, 256, 276, 300, 318, 324, 336, 340, 360, 366, 378, 414, 420, 438, 440, 444, 460, 462, 474, 480, 486

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

24 is 11000 in binary. This binary representation has three 0's and 3 divides 24. Also, the binary representation has two 1's and 2 also divides 24. So 24 is in the sequence.

Maple

filter:= proc(n) local L, x, m;
  L:= convert(n, base, 2);
  x:= convert(L, `+`);
  m:= nops(L);
  x < m and n mod x = 0 and n mod (m-x) = 0
end proc:
select(filter, [$1..1000]);

Mathematica

bdQ[n_]:=Module[{idn2=IntegerDigits[n, 2], x, y}, x=Count[idn2, 1]; y=Count[ idn2, 0]; If[x==0, x=n+1]; If[y==0, y=n+1]; And@@Divisible[n, {x, y}]]; Select[ Range[500], bdQ] (* Harvey P. Dale, Jan 22 2012 *)

Prog

(C) #include <stdio.h> int main(int argc, char *argv[]) { for(int n=1; n< 500 ; n++) { int digs[2] ; int nshifted=n ; digs[0]=digs[1]=0 ; while(nshifted) { digs[ nshifted & 1]++ ; nshifted >>= 1 ; } if ( digs[0] && digs[1]) if( ( n % digs[0]) == 0 && (n %digs[1]) ==0) printf("%d, ", n) ; } } /* R. J. Mathar, Apr 03 2006 */

Crossrefs

Cf. A049445, A117890. Includes A001146.

Sequence in context: A006093 A358816 A127965 * A262935 A178539 A072752

Adjacent sequences: A117888 A117889 A117890 * A117892 A117893 A117894

Keyword

easy,nonn,base

Author

Leroy Quet, Mar 30 2006

Extensions

More terms from R. J. Mathar, Apr 03 2006

Status

approved