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A038772 Numbers not divisible by any of their digits. 31
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 (list; graph; refs; listen; history; text; internal format)
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
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
CROSSREFS
Cf. A327561 (counts), A038770 (complement).
Cf. also A034709, A034837, A038769.
Sequence in context: A316724 A160774 A163142 * A188454 A178960 A282713
KEYWORD
base,easy,nonn,nice
AUTHOR
Henry Bottomley, May 04 2000
EXTENSIONS
Edited by N. J. A. Sloane, Nov 17 2008 at the suggestion of R. J. Mathar
STATUS
approved

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Last modified June 17 05:47 EDT 2024. Contains 373432 sequences. (Running on oeis4.)