A307636 Numbers k with property that no two divisors of k share a common digit.

1, 2, 3, 4, 5, 6, 7, 8, 9, 23, 27, 29, 37, 43, 47, 49, 53, 59, 67, 73, 79, 83, 86, 87, 89, 97, 223, 227, 229, 233, 239, 257, 263, 267, 269, 277, 283, 293, 307, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 409, 433, 439, 443, 449, 457, 463, 467, 479, 487, 499, 503

Offset: 1

Author

Giorgos Kalogeropoulos, May 03 2019

Keywords

• nonn
• base

Examples

			9566 is such a number because its divisors are  1, 2, 4783 and 9566, and no two of them share the same digit.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Giorgos Kalogeropoulos, Hostile Divisor Numbers, Code Golf, May 2019.

Crossrefs

A038603 is a subsequence.

Programs

Maple

filter:= proc(n) local D,i,j;
  D:= map(t -> convert(convert(t,base,10),set), convert(numtheory:-divisors(n),list));
  for i from 2 to nops(D) do
    for j from 1 to i-1 do
       if D[i] intersect D[j] <> {} then return false fi
  od od;
  true
end proc:
select(filter, [$1..1000]); # Robert Israel, Jul 07 2019

Mathematica

Select[Range@1000,!Or@@IntersectingQ@@@Subsets[IntegerDigits@Divisors[#],{2}]&]

PARI

isok(k) = {my(d = divisors(k), dd = apply(x->Set(digits(x)), d)); for (i=1, #dd, for (j=i+1, #dd, if (#setintersect(dd[i], dd[j]), return (0)););); return (1);} \\ Michel Marcus, Jul 07 2019

Python

from itertools import count, combinations, islice
from sympy import divisors
def A307636gen(): return filter(lambda n:all(len(set(s[0])&set(s[1])) == 0 for s in combinations((str(d) for d in divisors(n,generator=True)),2)),count(1))
A307636_list = list(islice(A307636gen(),20)) # Chai Wah Wu, Dec 08 2021