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

1,1

Comments

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A002808, A035139, A132080.

Sequence in context: A276628 A050695 A035139 * A062115 A141613 A072362

Adjacent sequences: A316224 A316225 A316226 * A316228 A316229 A316230

Keyword

nonn,base

Author

Jason Zimba, Jun 27 2018

Status

approved