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

1,1

Comments

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A038772, A382239.

Sequence in context: A153631 A382239 A382237 * A061754 A375595 A180066

Adjacent sequences: A082940 A082941 A082942 * A082944 A082945 A082946

Keyword

nonn,base

Author

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

Extensions

More terms from Harvey P. Dale, Oct 19 2016

Status

approved