A133598 Numbers k with all digits distinct and nonzero, such that none of k's digits divide k, but all the nonzero digits not in k do divide k.

5936, 45798, 45978, 47598, 47958, 49578, 49758, 54798, 57894, 58794, 58974, 59478, 59836, 59874, 74598, 74958, 75498, 78594, 78954, 79458, 79854, 85794, 87594, 87954, 89574, 94578, 94758, 95478, 95874, 97458, 97854, 98754, 346598, 358694

Offset

1,1

Comments

From Michael S. Branicky, Jul 06 2021: (Start)

No term contains 1 as a digit.

If 0 were allowed as a digit, then there would be 106104 terms, starting with 0, 5936, 9780, 37960, 45798 and ending with 987654203. (End)

References

Rodolfo Kurchan, Snark, December 2007

Links

Michael S. Branicky, Table of n, a(n) for n = 1..13272 (terms 1..100 from Rodolfo Kurchan)

Example

5936 is because 5936 is not divisible by 3, 5, 6 or 9 and is divisible by 1, 2, 4, 7 and 8.

Mathematica

addQ[n_]:=Module[{idn=IntegerDigits[n]}, FreeQ[idn, 0]&&Max[DigitCount[ n]] == 1&&Union[Divisible[n, idn]]=={False}&&And@@Divisible[n, Complement[ Range[ 9], idn]]]; Select[Range[400000], addQ] (* Harvey P. Dale, Oct 25 2017 *)

Prog

(Python)
def ok(n):
    s = str(n); ss = set(s)
    return '0' not in ss and len(s) == len(ss) and all(n%int(d) for d in ss) and all(n%int(d) == 0 for d in set("123456789")-ss)
answer2 = list(filter(ok, range(N))) # Michael S. Branicky, Jul 06 2021
(Python) # generates entire sequence
from sympy.utilities.iterables import multiset_permutations
def agen():
  for digits in range(1, 10):
    for mp in multiset_permutations("123456789", digits):
      n, mpc = int("".join(mp)), set("123456789") - set(mp)
      if all(n%int(d) for d in mp) and all(n%int(d) == 0 for d in mpc):
        yield n
print([an for an in agen()]) # Michael S. Branicky, Jul 06 2021

Crossrefs

Cf. A133606.

Sequence in context: A251464 A031575 A031755 * A028517 A289515 A186479

Adjacent sequences: A133595 A133596 A133597 * A133599 A133600 A133601

Keyword

nonn,base,fini,full

Author

Rodolfo Kurchan, Dec 27 2007

Extensions

Name clarified by Tanya Khovanova, Jul 06 2021

Status

approved