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A307636 Numbers k with property that no two divisors of k share a common digit. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified September 21 07:08 EDT 2019. Contains 327253 sequences. (Running on oeis4.)