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A093642
Numbers not containing all divisors in their binary representation.
5
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
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
Sequence in context: A110473 A105441 A325164 * A364566 A177733 A207675
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Apr 07 2004
STATUS
approved