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

Author

Jaroslav Krizek, Apr 17 2012

Keywords

• nonn
• base

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

Examples

			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.
		

Crossrefs

Subsequence of A034838. A116692 is a subsequence.

Cf. A209933.

Cf. A027751.

Cf. A027751.

Programs

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

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

Extensions

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