A090332 Numbers with no divisors >1 that are prefixes of other divisors in binary representation.

1, 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 33, 35, 37, 41, 43, 47, 49, 53, 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 89, 91, 97, 101, 103, 107, 109, 113, 121, 125, 127, 129, 131, 133, 137, 139, 141, 143, 145, 149, 151, 155, 157, 161, 163, 167, 169, 173, 179, 181

Offset: 1

Author

Reinhard Zumkeller, Nov 26 2003

Keywords

• nonn
• base

Comments

A090333 is a subsequence.

Complement of A090334.

Divisors >1 of a(n) in binary representation form a prefix code.

Examples

			Divisors >1 of a(188)=637: {7,13,49,91,637}, in binary: {111, 1101, 110001, 1011011, 1001111101}.
		

Links

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

Crossrefs

Cf. A090330, A090331, A090333, A090335, A088862.

Programs

Maple

filter:= proc(n) local d,  i,j;
  d:= numtheory:-divisors(n);
  for i in d do
    for j from 1 to ilog2(i)-1 do
      if member(floor(i/2^j), d) then return false fi
  od od;
  true
end proc:
select(filter, [$1..200]); # Robert Israel, Jul 08 2020

Mathematica

filterQ[n_] := Catch@Module[{d = Divisors[n], j}, Do[
     For[j = 1, j <= Floor@Log[2, i]-1, j++,
     If[MemberQ[d, Floor[i/2^j]], Throw[False]]], {i, d}];
     True];
Select[Range[200], filterQ] (* Jean-François Alcover, Dec 15 2021, after Robert Israel *)

Formula

A090330(a(n)) = 0.

A090331(a(n)) = 1.

Extensions

Missing term 121 inserted by Robert Israel, Jul 08 2020