A093642 Numbers not containing all divisors in their binary representation.

9, 15, 18, 21, 25, 27, 30, 33, 35, 36, 39, 42, 45, 49, 50, 51, 54, 57, 60, 63, 65, 66, 69, 70, 72, 75, 77, 78, 81, 84, 85, 87, 90, 91, 93, 95, 98, 99, 100, 102, 105, 108, 110, 111, 114, 115, 117, 119, 120, 121, 123, 125, 126, 129, 130, 132, 133, 135, 138, 140, 141

Offset

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

A093640(a(n)) < A000005(a(n)).

Example

55 is not a member, as the binary representations of 5 ("101") and 11 ("1011") both appear in the binary representation of 55 ("110111").

Mathematica

q[n_] := !AllTrue[Divisors[n], StringContainsQ[IntegerString[n, 2], IntegerString[#, 2]] &]; Select[Range[150], q] (* Amiram Eldar, Jun 05 2022 *)

Prog

(Haskell)
import Data.List (unfoldr, isInfixOf)
a093642 n = a093642_list !! (n-1)
a093642_list = filter
  (\x -> not $ all (`isInfixOf` b x) $ map b $ a027750_row x) [1..] where
  b = unfoldr (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 2)
-- Reinhard Zumkeller, Oct 27 2012
(Python)
from sympy import divisors
def ok(n):
    b = bin(n)[2:]
    return not all(bin(d)[2:] in b for d in divisors(n, generator=True))
print([k for k in range(119) if ok(k)]) # Michael S. Branicky, Jun 05 2022

Crossrefs

Complement of A123345.

Subsequence of A105441. - Reinhard Zumkeller, Apr 09 2005

Cf. A000005, A078822, A007088, A027750, A093640.

Sequence in context: A110473 A105441 A325164 * A364566 A177733 A207675

Adjacent sequences: A093639 A093640 A093641 * A093643 A093644 A093645

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 07 2004

Status

approved