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A093642 Numbers not containing all divisors in their binary representation.

%I A093642 #21 Jun 05 2022 08:27:15
%S A093642 9,15,18,21,25,27,30,33,35,36,39,42,45,49,50,51,54,57,60,63,65,66,69,
%T A093642 70,72,75,77,78,81,84,85,87,90,91,93,95,98,99,100,102,105,108,110,111,
%U A093642 114,115,117,119,120,121,123,125,126,129,130,132,133,135,138,140,141
%N A093642 Numbers not containing all divisors in their binary representation.
%H A093642 Reinhard Zumkeller, <a href="/A093642/b093642.txt">Table of n, a(n) for n = 1..10000</a>
%F A093642 A093640(a(n)) < A000005(a(n)).
%e A093642 55 is not a member, as the binary representations of 5 ("101") and 11 ("1011") both appear in the binary representation of 55 ("110111").
%t A093642 q[n_] := !AllTrue[Divisors[n], StringContainsQ[IntegerString[n, 2], IntegerString[#, 2]] &]; Select[Range[150], q] (* _Amiram Eldar_, Jun 05 2022 *)
%o A093642 (Haskell)
%o A093642 import Data.List (unfoldr, isInfixOf)
%o A093642 a093642 n = a093642_list !! (n-1)
%o A093642 a093642_list = filter
%o A093642   (\x -> not $ all (`isInfixOf` b x) $ map b $ a027750_row x) [1..] where
%o A093642   b = unfoldr (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 2)
%o A093642 -- _Reinhard Zumkeller_, Oct 27 2012
%o A093642 (Python)
%o A093642 from sympy import divisors
%o A093642 def ok(n):
%o A093642     b = bin(n)[2:]
%o A093642     return not all(bin(d)[2:] in b for d in divisors(n, generator=True))
%o A093642 print([k for k in range(119) if ok(k)]) # _Michael S. Branicky_, Jun 05 2022
%Y A093642 Complement of A123345.
%Y A093642 Subsequence of A105441. - _Reinhard Zumkeller_, Apr 09 2005
%Y A093642 Cf. A000005, A078822, A007088, A027750, A093640.
%K A093642 nonn,base
%O A093642 1,1
%A A093642 _Reinhard Zumkeller_, Apr 07 2004