login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A316227 Composite numbers k for which no nontrivial divisor shares any digits with k. 1
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 25 23:08 EST 2020. Contains 331270 sequences. (Running on oeis4.)