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A217973 Niven (or Harshad) numbers not containing the digit 0.

%I A217973 #29 Oct 21 2021 01:34:02
%S A217973 1,2,3,4,5,6,7,8,9,12,18,21,24,27,36,42,45,48,54,63,72,81,84,111,112,
%T A217973 114,117,126,132,133,135,144,152,153,156,162,171,192,195,198,216,222,
%U A217973 224,225,228,234,243,247,252,261,264,266,285,288,312,315,322,324,333,336
%N A217973 Niven (or Harshad) numbers not containing the digit 0.
%C A217973 Andreescu & Andrica prove that this sequence is infinite.
%C A217973 For each positive integer n, there exists a n-digit Niven (or Harshad) number not containing the digit 0 (see A348318 for more explanations and links). - _Bernard Schott_, Oct 20 2021
%D A217973 Titu Andreescu and Dorin Andrica, Number Theory, Structures, Examples, and Problems, Problem 5.2.3 on pages 109-110.
%H A217973 Charles R Greathouse IV, <a href="/A217973/b217973.txt">Table of n, a(n) for n = 1..10000</a>
%p A217973 filter:= proc(n) local L;
%p A217973 L:= convert(n,base,10);
%p A217973 not has(L,0) and n mod convert(L,`+`) = 0
%p A217973 end proc:
%p A217973 select(filter, [$1..1000]); # _Robert Israel_, Apr 01 2016
%t A217973 Select[Range[400], IntegerQ[ #/(Plus @@ IntegerDigits[#])] && DigitCount[#, 10, 0] == 0 &]  (* _Alonso del Arte_, Oct 16 2012 *)
%o A217973 (PARI) is(n)=vecsort(digits(n))[1]&&n%sumdigits(n)==0
%o A217973 (Python)
%o A217973 def ok(n): s = str(n); return '0' not in s and n%sum(map(int, s)) == 0
%o A217973 print([k for k in range(337) if ok(k)]) # _Michael S. Branicky_, Oct 20 2021
%Y A217973 Intersection of A005349 and A052382.
%Y A217973 A216405 is a subsequence.
%Y A217973 Cf. A348150, A348316, A348317, A348318.
%K A217973 nonn,base,easy
%O A217973 1,2
%A A217973 _Charles R Greathouse IV_, Oct 16 2012