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

1,2

Links

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

Giorgos Kalogeropoulos, Hostile Divisor Numbers, Code Golf, May 2019.

Example

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

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}]&]

Prog

(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

Crossrefs

A038603 is a subsequence.

Sequence in context: A272814 A322516 A132080 * A048386 A302503 A198044

Adjacent sequences: A307633 A307634 A307635 * A307637 A307638 A307639

Keyword

nonn,base

Author

Giorgos Kalogeropoulos, May 03 2019

Status

approved