A082943 Positive numbers not divisible by any of their digits nor by the sum of their digits.

23, 29, 34, 37, 38, 43, 46, 47, 49, 53, 56, 57, 58, 59, 67, 68, 69, 73, 74, 76, 78, 79, 83, 86, 87, 89, 94, 97, 98, 223, 227, 229, 233, 239, 249, 253, 257, 259, 263, 267, 269, 277, 283, 289, 293, 299, 323, 329, 334, 337, 338, 343, 346, 347, 349, 353, 356

Offset: 1

Author

Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 30 2003

Keywords

• nonn
• base

Comments

The definition implies that no digit is zero. - N. J. A. Sloane, Mar 27 2025

Examples

			38 is neither divisible by 3 nor 8 nor 11 (i.e. 3+8).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A038772, A382239.

Programs

Maple

filter:= proc(n) local L;
  L:= convert(n,base,10);
  not member(0,L) and not ormap(t -> n mod t = 0, [op(L),convert(L,`+`)])
end proc:
select(filter, [$1..1000]); # Robert Israel, Mar 19 2025

Mathematica

test1[n_] := Module[{dig = IntegerDigits[n]}, Union[Table[IntegerQ[n/dig[[i]]], {i, Length[dig]}]]] == {False};
test2[n_] := Module[{dig = IntegerDigits[n]}, Not[IntegerQ[n/Sum[dig[[i]], {i, Length[dig]}]]]];
Table[If[test1[n] && test2[n], n, 0], {n, 200}] // Union // Rest (* José María Grau Ribas, Feb 17 2010 *)
ndQ[n_]:=Module[{idn=IntegerDigits[n]},FreeQ[idn,0]&&NoneTrue[n/ Join[ idn, {Total[idn]}],IntegerQ]]; Select[Range[2000],ndQ] (* Harvey P. Dale, Oct 19 2016 *)

Extensions

More terms from Harvey P. Dale, Oct 19 2016