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A050695 Composite numbers k such that none of the prime factors of k is a substring of k. 6

%I #25 Aug 04 2021 02:22:06

%S 4,6,8,9,10,14,16,18,21,27,34,38,40,44,46,48,49,51,54,56,57,58,60,64,

%T 66,68,69,74,76,78,80,81,84,86,87,88,90,91,94,96,98,99,100,104,106,

%U 108,111,114,116,117,118,119,121,129,133,134,136,140,141,143,144,146

%N Composite numbers k such that none of the prime factors of k is a substring of k.

%C A131929(a(n)) = 0; together with 1, complement of A131930. - _Reinhard Zumkeller_, Jul 30 2007

%H Reinhard Zumkeller, <a href="/A050695/b050695.txt">Table of n, a(n) for n = 1..10000</a>

%e 114 = 2*3*19.

%t 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 *)

%t 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 *)

%Y Cf. A050694, A050696, A035139, A050698.

%K nonn,base,nice

%O 1,1

%A _Patrick De Geest_, Aug 15 1999

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