cp's OEIS Frontend

A382239 Numbers not divisible by any of their digits nor by the sum of their digits. Digit 0 is allowed (and does not divide anything).

%I A382239 #24 Apr 01 2025 17:53:01
%S A382239 23,29,34,37,38,43,46,47,49,53,56,57,58,59,67,68,69,73,74,76,78,79,83,
%T A382239 86,87,89,94,97,98,203,223,227,229,233,239,249,253,257,259,263,267,
%U A382239 269,277,283,289,293,299,307,323,329,334,337,338,343,346,347,349,353,356,358,359,367,373,374,376
%N A382239 Numbers not divisible by any of their digits nor by the sum of their digits.  Digit 0 is allowed (and does not divide anything).
%C A382239 From a suggestion by _Sergio Pimentel_.
%H A382239 Robert Israel, <a href="/A382239/b382239.txt">Table of n, a(n) for n = 1..10000</a>
%F A382239 n^k << a(n) < 2^n for n > 5 where k = log(10)/log(9). - _Charles R Greathouse IV_, Mar 20 2025
%e A382239 a(5) = 38 is included because 38 is not divisible by 3, 8 or 3 + 8 = 11.
%e A382239 a(30) = 203 is included because 203 is not divisible by 2, 0, 3 or 2 + 0 + 3 = 5.
%p A382239 filter:= proc(n) local L;
%p A382239   L:= subs(0=NULL,convert(n,base,10));
%p A382239   not ormap(t -> n mod t = 0, [op(L),convert(L,`+`)])
%p A382239 end proc:
%p A382239 select(filter, [$1..1000]);
%t A382239 s= {};Do[t=Select[IntegerDigits[n],#>0&];AppendTo[t,Total[t]];If[NoneTrue[t,Mod[n,#]==00&],AppendTo[s,n]],{n,376}];s (* _James C. McMahon_, Mar 21 2025 *)
%o A382239 (Python)
%o A382239 def ok(n):
%o A382239     d = list(map(int, str(n)))
%o A382239     return (s:=sum(d)) and n%s!=0 and all(n%di!=0 for di in set(d)-{0})
%o A382239 print([k for k in range(1, 377) if ok(k)]) # _Michael S. Branicky_, Apr 01 2025
%Y A382239 Subsequence of A052383.
%Y A382239 Cf. A038772, A082943, A382237.
%K A382239 nonn,base
%O A382239 1,1
%A A382239 _Robert Israel_, Mar 19 2025