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
KEYWORD
nonn,base
AUTHOR
Jason Zimba, Jun 27 2018
STATUS
approved