A123345 Numbers containing all divisors in their binary representation.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 19, 20, 22, 23, 24, 26, 28, 29, 31, 32, 34, 37, 38, 40, 41, 43, 44, 46, 47, 48, 52, 53, 55, 56, 58, 59, 61, 62, 64, 67, 68, 71, 73, 74, 76, 79, 80, 82, 83, 86, 88, 89, 92, 94, 96, 97, 101, 103, 104, 106, 107, 109, 112, 113, 116, 118

Offset: 1

Author

Reinhard Zumkeller, Oct 12 2006

Keywords

• nonn
• base

Links

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

Crossrefs

Complement of A093642. Different from A093641.

Cf. A000040 (subsequence), A027750, A218388.

Programs

Haskell

import Data.List (unfoldr, isInfixOf)
a123345 n = a123345_list !! (n-1)
a123345_list = filter
  (\x -> 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[100], q] (* Amiram Eldar, Jun 05 2022 *)

Python

from sympy import divisors
def ok(n):
    b = bin(n)[2:]
    return n and 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