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

1,2

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

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 *)

Crossrefs

Cf. A001248, A090332.

Sequence in context: A246328 A065772 A305755 * A137190 A044070 A348234

Adjacent sequences: A090330 A090331 A090332 * A090334 A090335 A090336

Keyword

nonn,base

Author

Reinhard Zumkeller, Nov 26 2003

Extensions

Missing term 121 inserted by Robert Israel, Jul 08 2020

Status

approved