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

1, 4, 6, 8, 9, 10, 14, 16, 18, 21, 27, 34, 38, 40, 44, 46, 48, 49, 54, 56, 57, 58, 60, 64, 66, 68, 69, 76, 78, 80, 81, 84, 86, 87, 88, 90, 96, 98, 99, 100, 106, 108, 111, 116, 118, 129, 134, 140, 144, 146, 148, 158, 160, 161, 166, 168, 174, 177, 180, 184, 188, 189, 196

Offset: 1

Author

Patrick De Geest, Nov 15 1998

Keywords

• nonn
• base

Examples

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

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A035140, A035141.

Programs

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

Maple

q:= n-> (f-> is(map(f, numtheory[factorset](n)) intersect
        {f(n)}={}))(d-> convert(d, base, 10)[]):
select(q, [$1..200])[];  # Alois P. Heinz, Oct 11 2021

Mathematica

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 *)

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);
isok(m) = my(df=digsf(m), d=digits(m)); (#setintersect(Set(df), Set(d)) == 0); \\ Michel Marcus, Oct 11 2021

Python

from sympy import factorint
def ok(n):
    return set(str(n)) & set("".join(str(p) for p in factorint(n))) == set()
print(list(filter(ok, range(1601))))  # Michael S. Branicky, Oct 11 2021

Extensions

Offset corrected and a(1) added by Giovanni Resta, May 02 2013