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 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

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