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A209933
Numbers that are divisible by all digits of their divisors.
2
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).
Any further terms are > 10^11. - Lucas A. Brown, Sep 29 2024
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
KEYWORD
nonn,base,more,hard
AUTHOR
Jaroslav Krizek, Apr 16 2012
STATUS
approved