A038772 Numbers not divisible by any of their digits.

23, 27, 29, 34, 37, 38, 43, 46, 47, 49, 53, 54, 56, 57, 58, 59, 67, 68, 69, 73, 74, 76, 78, 79, 83, 86, 87, 89, 94, 97, 98, 203, 207, 209, 223, 227, 229, 233, 239, 247, 249, 253, 257, 259, 263, 267, 269, 277, 283, 289, 293, 299, 307, 308, 323, 329, 334, 337, 338

Offset: 1

Author

Henry Bottomley, May 04 2000

Keywords

• base
• easy
• nonn
• nice

Comments

A038769(a(n)) = 0; complement of A038770.

This is a regular language when written in decimal, though the minimal regular expression is probably thousands of characters long. - Charles R Greathouse IV, Aug 19 2011

Exponential density 0.954... = A104139. Asymptotically 8/35 * n^0.954... + O(n^0.903...) members up to n. - Charles R Greathouse IV, Jul 22 2012

Examples

			34 is divisible by neither 3 nor 4.
35 is excluded because 5 is a divisor of 35, but 37 is included because neither 3 nor 7 is a divisor of 37
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for 10-automatic sequences

Crossrefs

Cf. A327561 (counts), A038770 (complement).

Cf. also A034709, A034837, A038769.

Programs

Haskell

import Data.Char (digitToInt)
a038772 n = a038772_list !! (n-1)
a038772_list = filter p [1..] where
   p n = all (> 0) $ map ((mod n) . digitToInt) $ filter (> '0') $ show n
-- Reinhard Zumkeller, Jun 19 2011

Magma

[k:k in [1..340]| forall{c:c in Set(Intseq(k)) diff {0}|k mod c ne 0}]; // Marius A. Burtea, Dec 22 2019

Mathematica

nddQ[n_]:=Module[{idn=DeleteCases[IntegerDigits[n],0]},And@@Table[ !Divisible[n, idn[[i]]],{i,Length[idn]}]]; Select[Range[350],nddQ] (* Harvey P. Dale, Nov 01 2011 *)

PARI

is(n)=my(v=vecsort(eval(Vec(Str(n))), , 8)); for(i=if(v[1], 1, 2), #v, if(n%v[i]==0, return(0))); 1 \\ Charles R Greathouse IV, Jul 22 2011

Python

def ok(n): return not any(n%int(d) == 0 for d in str(n) if d != '0')
print(list(filter(ok, range(1, 339)))) # Michael S. Branicky, May 20 2021

Extensions

Edited by N. J. A. Sloane, Nov 17 2008 at the suggestion of R. J. Mathar