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%I #4 May 15 2017 13:30:54
%S 165,273,345,385,399,435,561,595,651,665,715,759,777,795,885,903,957,
%T 1001,1015,1065,1085,1173,1209,1235,1281,1335,1435,1443,1463,1495,
%U 1515,1533,1547,1551,1615,1645,1659,1677,1705,1749,1767,1771,1885,1947,1965
%N Numbers that are the product of 3 distinct primes a,b and c, such that a+b+c are prime numbers.
%C 165=3*5*11; 3+5+11=19,...
%H Harvey P. Dale, <a href="/A176877/b176877.txt">Table of n, a(n) for n = 1..1000</a>
%t l[n_]:=Last/@FactorInteger[n]; f[n_]:=First/@FactorInteger[n]; lst={};Do[If[l[n]=={1,1,1},a=f[n][[1]];b=f[n][[2]];c=f[n][[3]];If[PrimeQ[a+b+c],AppendTo[lst,n]]],{n,7!}];lst
%t With[{upto=2000},Select[Times@@@Select[Subsets[Prime[Range[ PrimePi[ upto/6]]],{3}],PrimeQ[Total[#]]&]//Union,#<=upto&]] (* _Harvey P. Dale_, May 15 2017 *)
%Y Cf. A006881, A014574, A176875, A176876
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Apr 27 2010
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