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A316227
Composite numbers k for which no nontrivial divisor shares any digits with k.
2
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
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