A182183 Numbers k such that the divisors of k are divisible by all digits of their divisors.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 22, 24, 33, 44, 55, 66, 77, 88, 99, 132, 264, 1111111111111111111, 2222222222222222222, 3333333333333333333, 4444444444444444444, 5555555555555555555, 6666666666666666666, 7777777777777777777, 8888888888888888888

Offset

1,2

Comments

Subsequence of A209933 (numbers that are divisible by all digits of their divisors).

All divisors of numbers in this sequence are also in the sequence.

The primitive elements of this sequence are A116692. No member of this sequence is divisible by a prime outside this sequence. - Charles R Greathouse IV, Apr 17 2012

Links

Table of n, a(n) for n=1..31.

Example

Number 48 with divisors 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 is not in the sequence because 6 is not a divisor of 16.

Prog

(PARI) all(n)=my(v=vecsort(eval(Vec(Str(n))), , 8)); if(v[1]==0, return(0)); for(i=1, #v, if(n%v[i], return(0))); 1
is(n)=fordiv(n, d, if(!all(d), return(0))); 1 \\ Charles R Greathouse IV, Apr 17 2012
(Haskell)
import Data.List ((\\))
a182183 n = a182183_list !! (n-1)
a182183_list = f a209933_list [1] where
   f (x:xs) ys =
     if null (a027751_row x \\ ys) then x : f xs (x : ys) else f xs ys
-- Reinhard Zumkeller, Apr 19 2012

Crossrefs

Subsequence of A034838. A116692 is a subsequence.

Cf. A209933.

Cf. A027751.

Cf. A027751.

Sequence in context: A034838 A063527 A209933 * A308472 A064700 A180484

Adjacent sequences: A182180 A182181 A182182 * A182184 A182185 A182186

Keyword

nonn,base

Author

Jaroslav Krizek, Apr 17 2012

Extensions

a(24)-a(31) from Charles R Greathouse IV, Apr 17 2012

Status

approved