A082943 -id:A082943 - 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).

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, 203, 223, 227, 229, 233, 239, 249, 253, 257, 259, 263, 267, 269, 277, 283, 289, 293, 299, 307, 323, 329, 334, 337, 338, 343, 346, 347, 349, 353, 356, 358, 359, 367, 373, 374, 376

Offset: 1

Robert Israel, Mar 19 2025

From a suggestion by Sergio Pimentel.

			a(5) = 38 is included because 38 is not divisible by 3, 8 or 3 + 8 = 11.
a(30) = 203 is included because 203 is not divisible by 2, 0, 3 or 2 + 0 + 3 = 5.

Robert Israel, Table of n, a(n) for n = 1..10000

Subsequence of A052383.

Cf. A038772, A082943, A382237.

filter:= proc(n) local L;
  L:= subs(0=NULL,convert(n,base,10));
  not ormap(t -> n mod t = 0, [op(L),convert(L,`+`)])
end proc:
select(filter, [$1..1000]);

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 *)

def ok(n):
    d = list(map(int, str(n)))
    return (s:=sum(d)) and n%s!=0 and all(n%di!=0 for di in set(d)-{0})
print([k for k in range(1, 377) if ok(k)]) # Michael S. Branicky, Apr 01 2025

n^k << a(n) < 2^n for n > 5 where k = log(10)/log(9). - Charles R Greathouse IV, Mar 20 2025

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

Original entry on oeis.org

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, 203, 223, 227, 229, 233, 239, 249, 253, 257, 263, 267, 269, 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

Offset: 1

Sergio Pimentel, Mar 19 2025

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.

Conjecture: after a sufficiently large n this sequence grows faster than the prime numbers.

			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.
289 is not in the sequence because it can be divided by (8+9)=17.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A082943, A038772, A005349, A065877, A228017, A382239.

filter:= proc(n) local L,S;
  L:= convert(n,base,10);
  andmap(s -> s=0 or n mod s <> 0, map(convert,combinat:-choose(L),`+`))
end proc:
select(filter, [$1..1000]); # Robert Israel, Mar 19 2025

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

from itertools import chain, combinations
def powerset(s): # skipping empty set
    return chain.from_iterable(combinations(s, r) for r in range(1, len(s)+1))
def ok(n): return all(n%t!=0 for s in powerset(list(map(int, str(n)))) if (t:=sum(s))>0)
print([k for k in range(1, 404) if ok(k)]) # Michael S. Branicky, Apr 01 2025

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).

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