This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
51 = 3*17 -> digit 1 appears in 5{1}.
295 = 5 * 59 since {5,9} is a subset of {2,5,9}.
id[n_]:=Complement[Range[0,9],IntegerDigits[n]]; fac[n_]:=Flatten[IntegerDigits[Take[FactorInteger[n],All,1]]]; t={}; Do[If[!PrimeQ[n] && Intersection[id[n],fac[n]] == {}, AppendTo[t,n]], {n,2,1380}]; t (* Jayanta Basu, May 01 2013 *)
Select[Range@10000, CompositeQ@# && SubsetQ[IntegerDigits@#,Flatten@IntegerDigits@(#[[1]] & /@ FactorInteger@#)] &] (* Hans Rudolf Widmer, May 11 2023 *)
from sympy import factorint, isprime
def ok(n): return n > 1 and not isprime(n) and set("".join(str(p) for p in factorint(n))) <= set(str(n))
print([k for k in range(1380) if ok(k)]) # Michael S. Branicky, May 11 2023
114 = 2*3*19.
d[n_]:=IntegerDigits[n]; t={}; Do[le1=Max@@Length/@(t1=d[First/@FactorInteger[n]]); t2=Flatten[Table[Partition[d[n],i,1],{i,le1}],1]; If[!PrimeQ[n]&&Intersection[t1,t2]=={},AppendTo[t,n]],{n,2,146}]; t (* Jayanta Basu, May 31 2013 *)
npfsQ[n_]:=Module[{idn=IntegerDigits[n],f=FactorInteger[n][[All,1]]}, And@@ Table[SequenceCount[idn,IntegerDigits[f[[i]]]]==0,{i, Length[ f]}]]; Select[Range[200],CompositeQ[#] && npfsQ[#]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 28 2016 *)
1972 = {1,2,7,9} -> 2 * 2 * 17 * 29, so 1972 is a term.
Fac[n_]:=Sort[DeleteDuplicates[Flatten[IntegerDigits[Take[FactorInteger[n], All,1]]]]];Fn[n_]:=Sort[DeleteDuplicates[IntegerDigits[n]]];t={};Do[If[! PrimeQ[n]&&Fac[n]===Fn[n],AppendTo[t, n]],{n,2,15100}];t (* Jayanta Basu, May 02 2013 *)
is(n)=if(isprime(n)||n<9,return(0));my(f=factor(n)[,1],v=[]);for(i=1,#f,v=concat(v,digits(f[i])));vecsort(digits(n),,8)==vecsort(v,,8) \\ Charles R Greathouse IV, May 02 2013
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.
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
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 *)
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
158 = 2 * 79 since {2,7,9} do not appear in {1,5,8} and both have 3 digits.
q[n_] := Module[{d = IntegerDigits[n], f = FactorInteger[n]}, Length[d] == Plus @@ ((Last[#]*IntegerLength[First[#]]) & /@ f ) && Intersection[d, Join @@ IntegerDigits[f[[;; , 1]]]] == {}]; Select[Range[1600], q] (* Amiram Eldar, Oct 12 2021 *)
digsf(n) = my(f=factor(n), list=List()); for (k=1, #f~, my(dk=digits(f[k,1])); for (i=1, f[k,2], for (j=1, #dk, listput(list, dk[j])))); Vec(list); isokd(m) = my(df=digsf(m), d=digits(m)); (#df == #d) && (#setintersect(Set(df), Set(d)) == 0); \\ Michel Marcus, Oct 11 2021
from sympy import factorint
def ok(n):
s, f = str(n), factorint(n)
pfd = set("".join(str(p) for p in f))
if set(s) & pfd != set(): return False
return len(s) == sum(len(str(p))*f[p] for p in f)
print(list(filter(ok, range(1601)))) # Michael S. Branicky, Oct 11 2021
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