cp's OEIS Frontend

A382237 Numbers that are not divisible by the sum of any subset of their digits.

%I A382237 #27 Apr 02 2025 10:25:49
%S A382237 23,29,34,37,38,43,46,47,49,53,56,57,58,59,67,68,69,73,74,76,78,79,83,
%T A382237 86,87,89,94,97,98,203,223,227,229,233,239,249,253,257,263,267,269,
%U A382237 277,283,293,299,307,323,329,334,337,338,346,347,349,353,356,358,359,367,373,376,377,379,380,383,386,388,389,394,397,398,403
%N A382237 Numbers that are not divisible by the sum of any subset of their digits.
%C A382237 This sequence has density zero since no numbers with the digit '1' are in it.  The sequence is infinite. Example: Numbers like 23, 203, 2003, 20003, etc. are included because none of them is divisible by 2, 3, or 5.
%C A382237 Conjecture: after a sufficiently large n this sequence grows faster than the prime numbers.
%H A382237 Michael S. Branicky, <a href="/A382237/b382237.txt">Table of n, a(n) for n = 1..10000</a>
%e A382237 358 is in the sequence because it can't be divided by 3, 5, 8, (3+5)=8, (3+8)=11, (5+8)=13 or (3+5+8)=16.
%e A382237 289 is not in the sequence because it can be divided by (8+9)=17.
%p A382237 filter:= proc(n) local L,S;
%p A382237   L:= convert(n,base,10);
%p A382237   andmap(s -> s=0 or n mod s <> 0, map(convert,combinat:-choose(L),`+`))
%p A382237 end proc:
%p A382237 select(filter, [$1..1000]); # _Robert Israel_, Mar 19 2025
%o A382237 (PARI) isok(k) = my(d=digits(k)); forsubset(#d, s, my(ss=sum(i=1, #s, d[s[i]])); if (ss && !(k % sum(i=1, #s, d[s[i]])), return(0))); return(1); \\ _Michel Marcus_, Mar 27 2025
%o A382237 (Python)
%o A382237 from itertools import chain, combinations
%o A382237 def powerset(s): # skipping empty set
%o A382237     return chain.from_iterable(combinations(s, r) for r in range(1, len(s)+1))
%o A382237 def ok(n): return all(n%t!=0 for s in powerset(list(map(int, str(n)))) if (t:=sum(s))>0)
%o A382237 print([k for k in range(1, 404) if ok(k)]) # _Michael S. Branicky_, Apr 01 2025
%Y A382237 Cf. A082943, A038772, A005349, A065877, A228017, A382239.
%K A382237 nonn,base
%O A382237 1,1
%A A382237 _Sergio Pimentel_, Mar 19 2025