A038772 - OEIS

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

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OFFSET

1,1

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for 10-automatic sequences

EXAMPLE

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

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 *)

PROG

(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

(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

(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

(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