A209933 Numbers that are divisible by all digits of their divisors.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 22, 24, 33, 44, 48, 55, 66, 77, 88, 99, 132, 264

Offset: 1

Author

Jaroslav Krizek, Apr 16 2012

Keywords

• nonn
• base
• more
• hard

Comments

There are 24 terms < 10000. Conjecture: next term a(25) = prime repunit with 19 digits 1.

Supersequence of A004022 (prime repunits). Subsequence of A034838 (numbers k that are divisible by every digit of k).

Any further terms are > 10^11. - Lucas A. Brown, Sep 29 2024

Examples

			Number 264 with divisors 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264 is in sequence because all possible digits its divisors (1, 2, 3, 4, 6, 8) are its divisors.
		

Links

• Lucas A. Brown, Python program.

Crossrefs

Cf. A004022, A034838, A037278.

Cf. A027750.

Programs

Haskell

import Data.List (unfoldr, nub, sort)
a209933 n = a209933_list !! (n-1)
a209933_list = filter f [1..] where
   f x = head (ds x) /= 0 && all (== 0) (map ((mod x)) (ds x)) where
     ds = sort . nub . concatMap (unfoldr (\z ->
          if z == 0 then Nothing else Just $ swap $ divMod z 10)) .
          a027750_row
-- Reinhard Zumkeller, Apr 19 2012