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

Author

Reinhard Zumkeller, Apr 07 2004

Keywords

• nonn
• base

Examples

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

Links

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

Crossrefs

Complement of A123345.

Subsequence of A105441. - Reinhard Zumkeller, Apr 09 2005

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

Programs

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

Mathematica

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

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

Formula

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