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

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, 114, 117, 126, 132, 133, 135, 144, 152, 153, 156, 162, 171, 192, 195, 198, 216, 222, 224, 225, 228, 234, 243, 247, 252, 261, 264, 266, 285, 288, 312, 315, 322, 324, 333, 336

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

Intersection of A005349 and A052382.

A216405 is a subsequence.

Cf. A348150, A348316, A348317, A348318.

Sequence in context: A343680 A114440 A334416 * A097518 A097569 A308561

Adjacent sequences: A217970 A217971 A217972 * A217974 A217975 A217976

Keyword

nonn,base,easy

Author

Charles R Greathouse IV, Oct 16 2012

Status

approved