OFFSET
1,2
COMMENTS
Andreescu & Andrica prove that this sequence is infinite.
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
REFERENCES
Titu Andreescu and Dorin Andrica, Number Theory, Structures, Examples, and Problems, Problem 5.2.3 on pages 109-110.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
MAPLE
filter:= proc(n) local L;
L:= convert(n, base, 10);
not has(L, 0) and n mod convert(L, `+`) = 0
end proc:
select(filter, [$1..1000]); # Robert Israel, Apr 01 2016
MATHEMATICA
Select[Range[400], IntegerQ[ #/(Plus @@ IntegerDigits[#])] && DigitCount[#, 10, 0] == 0 &] (* Alonso del Arte, Oct 16 2012 *)
PROG
(PARI) is(n)=vecsort(digits(n))[1]&&n%sumdigits(n)==0
(Python)
def ok(n): s = str(n); return '0' not in s and n%sum(map(int, s)) == 0
print([k for k in range(337) if ok(k)]) # Michael S. Branicky, Oct 20 2021
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Charles R Greathouse IV, Oct 16 2012
STATUS
approved