A217973 - OEIS

%I #29 Oct 21 2021 01:34:02

%S 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 114,117,126,132,133,135,144,152,153,156,162,171,192,195,198,216,222,

%U 224,225,228,234,243,247,252,261,264,266,285,288,312,315,322,324,333,336

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

%C Andreescu & Andrica prove that this sequence is infinite.

%C 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 Titu Andreescu and Dorin Andrica, Number Theory, Structures, Examples, and Problems, Problem 5.2.3 on pages 109-110.

%H Charles R Greathouse IV, <a href="/A217973/b217973.txt">Table of n, a(n) for n = 1..10000</a>

%p filter:= proc(n) local L;

%p L:= convert(n,base,10);

%p not has(L,0) and n mod convert(L,`+`) = 0

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Apr 01 2016

%t Select[Range[400], IntegerQ[ #/(Plus @@ IntegerDigits[#])] && DigitCount[#, 10, 0] == 0 &]  (* _Alonso del Arte_, Oct 16 2012 *)

%o (PARI) is(n)=vecsort(digits(n))[1]&&n%sumdigits(n)==0

%o (Python)

%o def ok(n): s = str(n); return '0' not in s and n%sum(map(int, s)) == 0

%o print([k for k in range(337) if ok(k)]) # _Michael S. Branicky_, Oct 20 2021

%Y Intersection of A005349 and A052382.

%Y A216405 is a subsequence.

%Y Cf. A348150, A348316, A348317, A348318.

%K nonn,base,easy

%O 1,2

%A _Charles R Greathouse IV_, Oct 16 2012