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

1,2

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).

Links

Table of n, a(n) for n=1..24.

Example

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.

Prog

(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

Crossrefs

Cf. A004022, A034838, A037278.

Cf. A027750.

Sequence in context: A337184 A034838 A063527 * A182183 A308472 A064700

Adjacent sequences: A209930 A209931 A209932 * A209934 A209935 A209936

Keyword

nonn,base,more

Author

Jaroslav Krizek, Apr 16 2012

Status

approved