A316227 Composite numbers k for which no nontrivial divisor shares any digits with k.

4, 6, 8, 9, 10, 14, 16, 18, 21, 27, 34, 38, 46, 49, 54, 56, 57, 58, 68, 69, 76, 78, 81, 86, 87, 106, 111, 116, 118, 129, 134, 146, 158, 161, 166, 177, 188, 201, 219, 247, 249, 259, 267, 289, 323, 329, 334, 356, 358, 388, 413, 446, 454, 458, 466, 477, 478, 489

Offset: 1

Author

Jason Zimba, Jun 27 2018

Keywords

• nonn
• base

Comments

A nontrivial divisor of k means a divisor greater than 1 and less than k.

Examples

			The nontrivial divisors of 54 are 2, 3, 6, 9, 18, and 27, none of which have a digit 5 or 4.
The nontrivial divisors of 248629501 are 337 and 737773.
The nontrivial divisors of 321810649 are 557 and 577757.
		

Links

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

Crossrefs

Cf. A002808, A035139, A132080.

Programs

Maple

filter:= proc(n) local S;
  if isprime(n) then return false fi;
  S:= convert(convert(n,base,10),set);
  andmap(d -> convert(convert(d,base,10),set) intersect S = {}, numtheory:-divisors(n) minus {1,n})
end proc:
select(filter, [$4..1000]); # Robert Israel, Jul 22 2018

Mathematica

MaxCheck = 1000; (* modify as desired *)
ResultList = {};
Do[
  If[
   Not[PrimeQ[k]] &&
    Intersection[
      Flatten[
       Map[
        IntegerDigits,
        Complement[Divisors[k], {1, k}]
        ]
       ],
      IntegerDigits[k]
      ] == {},
   ResultList = Append[ResultList, k]
   ],
  {k, 2, MaxCheck}];
ResultList
(* or *) Select[Range@500, CompositeQ@# && Intersection[ IntegerDigits@#, Flatten@ IntegerDigits@ Most@ Rest@ Divisors@ #] == {} &] (* Giovanni Resta, Jun 27 2018 *)

PARI

isok(n) = {my(d=divisors(n), dd = Set(digits(n))); for (k=2, #d-1, if (#setintersect(Set(digits(d[k])), dd), return (0));); return (1);}
lista(nn) = {forcomposite(n=1, nn, if (isok(n), print1(n, ", ")););} \\ Michel Marcus, Jul 03 2018