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

%I A082943 #22 Mar 27 2025 10:21:40
%S A082943 23,29,34,37,38,43,46,47,49,53,56,57,58,59,67,68,69,73,74,76,78,79,83,
%T A082943 86,87,89,94,97,98,223,227,229,233,239,249,253,257,259,263,267,269,
%U A082943 277,283,289,293,299,323,329,334,337,338,343,346,347,349,353,356
%N A082943 Positive numbers not divisible by any of their digits nor by the sum of their digits.
%C A082943 The definition implies that no digit is zero. - _N. J. A. Sloane_, Mar 27 2025
%H A082943 Harvey P. Dale, <a href="/A082943/b082943.txt">Table of n, a(n) for n = 1..1000</a>
%e A082943 38 is neither divisible by 3 nor 8 nor 11 (i.e. 3+8).
%p A082943 filter:= proc(n) local L;
%p A082943   L:= convert(n,base,10);
%p A082943   not member(0,L) and not ormap(t -> n mod t = 0, [op(L),convert(L,`+`)])
%p A082943 end proc:
%p A082943 select(filter, [$1..1000]); # _Robert Israel_, Mar 19 2025
%t A082943 test1[n_] := Module[{dig = IntegerDigits[n]}, Union[Table[IntegerQ[n/dig[[i]]], {i, Length[dig]}]]] == {False};
%t A082943 test2[n_] := Module[{dig = IntegerDigits[n]}, Not[IntegerQ[n/Sum[dig[[i]], {i, Length[dig]}]]]];
%t A082943 Table[If[test1[n] && test2[n], n, 0], {n, 200}] // Union // Rest (* _José María Grau Ribas_, Feb 17 2010 *)
%t A082943 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 *)
%Y A082943 Cf. A038772, A382239.
%K A082943 nonn,base
%O A082943 1,1
%A A082943 Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 30 2003
%E A082943 More terms from _Harvey P. Dale_, Oct 19 2016