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%I #10 Jun 29 2021 14:52:51
%S 1105,1130,1462,1644,1742,1767,2014,2222,2232,2260,2337,2365,2397,
%T 2464,2541,2667,2684,2697,2702,2755,2821,2914,3074,3115,3195,3289,
%U 3332,3477,3484,3514,3552,3619,3657,3685,3782,3783,3842,3965,4014,4088,4122,4147,4277
%N Numbers n such that n,n+1 and sum of this two numbers have at least 3 distinct prime factors.
%e 1105 = 5*13*17, 1106 = 2*7*79, 1105 + 1106 = 2211 = 3*11*67.
%p q:= n-> andmap(x-> nops(numtheory[factorset](x))>2, [n, n+1, 2*n+1]):
%p select(q, [$1..4600])[]; # _Alois P. Heinz_, Jun 29 2021
%t f[n_]:=Length[FactorInteger[n]]; lst={};Do[If[f[n]>=3&&f[n+1]>=3&&f[n+n+1]>=3,AppendTo[lst,n]],{n,8!}];lst
%Y Cf. A140077, A140078, A168626, A168628.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Dec 01 2009
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