A035139 - OEIS

%I #29 Sep 08 2022 08:44:52

%S 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 66,68,69,76,78,80,81,84,86,87,88,90,96,98,99,100,106,108,111,116,118,

%U 129,134,140,144,146,148,158,160,161,166,168,174,177,180,184,188,189,196

%N Digits of prime factors of k do not appear in k.

%H Michael S. Branicky, <a href="/A035139/b035139.txt">Table of n, a(n) for n = 1..10000</a>

%e 161 = 7 * 23 since {2,3,7} and {1,6} are separate digit sets.

%p q:= n-> (f-> is(map(f, numtheory[factorset](n)) intersect

%p         {f(n)}={}))(d-> convert(d, base, 10)[]):

%p select(q, [$1..200])[];  # _Alois P. Heinz_, Oct 11 2021

%t 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 (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 (Python)

%o from sympy import factorint

%o def ok(n):

%o     return set(str(n)) & set("".join(str(p) for p in factorint(n))) == set()

%o print(list(filter(ok, range(1601))))  # _Michael S. Branicky_, Oct 11 2021

%o (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 isok(m) = my(df=digsf(m), d=digits(m)); (#setintersect(Set(df), Set(d)) == 0); \\ _Michel Marcus_, Oct 11 2021

%Y Cf. A035140, A035141.

%K nonn,base

%O 1,2

%A _Patrick De Geest_, Nov 15 1998

%E Offset corrected and a(1) added by _Giovanni Resta_, May 02 2013