A090333 Nonprimes with no divisors >1 that are prefixes of other divisors in binary representation.

1, 9, 25, 33, 35, 49, 65, 69, 77, 91, 121, 125, 129, 133, 141, 143, 145, 155, 161, 169, 209, 247, 259, 265, 267, 287, 289, 295, 299, 301, 305, 319, 323, 329, 341, 343, 361, 371, 377, 391, 395, 403, 407, 437, 451, 473, 481, 485, 493, 505, 515, 519, 527, 529, 533

Offset: 1

Author

Reinhard Zumkeller, Nov 26 2003

Keywords

• nonn
• base

Comments

A090332 without primes.

Includes all members of A001248 except 4. - Robert Israel, Jul 08 2020

Links

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

Crossrefs

Cf. A001248, A090332.

Programs

Maple

filter:= proc(n) local d,  i,j;
  if isprime(n) then return false fi;
  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, [seq(i,i=1..1000,2)]); # Robert Israel, Jul 08 2020

Mathematica

filterQ[n_] := If[PrimeQ[n], False, 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[1000], filterQ] (* Jean-François Alcover, Dec 16 2021, after Robert Israel *)

Extensions

Missing term 121 inserted by Robert Israel, Jul 08 2020