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A123345
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Numbers containing all divisors in their binary representation.
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5
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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
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OFFSET
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1,2
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LINKS
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MATHEMATICA
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q[n_] := AllTrue[Divisors[n], StringContainsQ[IntegerString[n, 2], IntegerString[#, 2]] &]; Select[Range[100], q] (* Amiram Eldar, Jun 05 2022 *)
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PROG
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(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)
(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))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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