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A035139 Digits of prime factors of k do not appear in k.

%I A035139 #29 Sep 08 2022 08:44:52
%S A035139 1,4,6,8,9,10,14,16,18,21,27,34,38,40,44,46,48,49,54,56,57,58,60,64,
%T A035139 66,68,69,76,78,80,81,84,86,87,88,90,96,98,99,100,106,108,111,116,118,
%U A035139 129,134,140,144,146,148,158,160,161,166,168,174,177,180,184,188,189,196
%N A035139 Digits of prime factors of k do not appear in k.
%H A035139 Michael S. Branicky, <a href="/A035139/b035139.txt">Table of n, a(n) for n = 1..10000</a>
%e A035139 161 = 7 * 23 since {2,3,7} and {1,6} are separate digit sets.
%p A035139 q:= n-> (f-> is(map(f, numtheory[factorset](n)) intersect
%p A035139         {f(n)}={}))(d-> convert(d, base, 10)[]):
%p A035139 select(q, [$1..200])[];  # _Alois P. Heinz_, Oct 11 2021
%t A035139 Fac[n_] := Flatten[IntegerDigits[Take[FactorInteger[n],All,1]]]; t={1}; Do[ If[!PrimeQ[n] && Intersection[Fac[n], IntegerDigits[n]] == {}, AppendTo[t,n]], {n,2,196}]; t (* _Jayanta Basu_, May 02 2013 *)
%o A035139 (Magma) [k:k in [1..200]| forall{a: a in PrimeDivisors(k)|Set(Intseq(a)) meet Set(Intseq(k)) eq {}}]; // _Marius A. Burtea_, Oct 08 2019
%o A035139 (Python)
%o A035139 from sympy import factorint
%o A035139 def ok(n):
%o A035139     return set(str(n)) & set("".join(str(p) for p in factorint(n))) == set()
%o A035139 print(list(filter(ok, range(1601))))  # _Michael S. Branicky_, Oct 11 2021
%o A035139 (PARI) 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);
%o A035139 isok(m) = my(df=digsf(m), d=digits(m)); (#setintersect(Set(df), Set(d)) == 0); \\ _Michel Marcus_, Oct 11 2021
%Y A035139 Cf. A035140, A035141.
%K A035139 nonn,base
%O A035139 1,2
%A A035139 _Patrick De Geest_, Nov 15 1998
%E A035139 Offset corrected and a(1) added by _Giovanni Resta_, May 02 2013