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%I #52 Oct 02 2020 16:58:38
%S 2121,3011,3963,6125,7631,8173,8275,8649,8781,10519,10851,11383,11599,
%T 11883,12001,12163,12271,12789,12807,13749,14509,15381,15705,15959,
%U 16583,16761,17163,17473,17787,18813,19283,19831,19937,20483,20513,20633,21673,22121
%N Numbers n for which the numbers 6n+1, 3n+2, 6n+7 are all odd composite squarefree numbers, but none are semiprimes.
%H Peter J. C. Moses, <a href="/A263510/b263510.txt">Table of n, a(n) for n = 1..2000</a>
%t semiPrimeQ:=Last[Total[FactorInteger[#]]]==2&;
%t A263510=Select[Range[10000],Apply[And,Map[CompositeQ[#]&&OddQ[#]&&SquareFreeQ[#]&&(!semiPrimeQ[#])&,{6#+1,3#+2,6#+7}]]&]
%t csnQ[n_]:=Module[{c={6n+1,3n+2,6n+7}},AllTrue[c,CompositeQ]&&AllTrue[ c,SquareFreeQ]&&AllTrue[c,OddQ]&&FreeQ[PrimeOmega[c],2]]; Select[Range[ 22200],csnQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Oct 02 2020 *)
%Y Cf. A001358, A264778, A264779.
%K nonn
%O 1,1
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Nov 24 2015