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A274433 Products of two distinct tribonacci numbers > 1.

%I A274433 #4 Jun 22 2016 23:16:38
%S A274433 15,27,45,51,85,93,153,155,171,279,285,315,513,525,527,579,945,965,
%T A274433 969,1065,1737,1767,1775,1785,1959,3195,3255,3265,3281,3603,5877,5983,
%U A274433 5985,6005,6035,6627,10809,11001,11005,11045,11101,12189,19881,20235,20243
%N A274433 Products of two distinct tribonacci numbers > 1.
%C A274433 Are these unique among all products of distinct tribonacci numbers (A000213)?  (See A274432.)
%e A274433 The tribonacci numbers > 1 are 3,5,9,17,31,57,..., so that the binary products in increasing order are 15, 27,45, 51, 85, ...
%t A274433 r[1] := 1; r[2] := 1; r[3] = 1; r[n_] := r[n] = r[n - 1] + r[n - 2] + r[n - 3];
%t A274433 s = {1}; z = 60; f = Map[r, Range[z]]; Take[f, 20]
%t A274433 Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}];
%t A274433 Take[s, 2 z]  (* A274432 *)
%t A274433 infQ[n_] := MemberQ[f, n];
%t A274433 ans = Table[#[[Flatten[Position[Map[Apply[Times, #] &, #], s[[n]]]][[1]]]] &[
%t A274433 Rest[Subsets[Map[#[[1]] &, Select[Map[{#, infQ[#]} &, Divisors[s[[n]]]], #[[2]] && #[[1]] > 1 &]]]]], {n, 2, 300}];
%t A274433 Map[Apply[Times, #] &, Select[ans, Length[#] == 2 &]] (* A274433 *)
%t A274433 Map[Apply[Times, #] &, Select[ans, Length[#] == 3 &]] (* A274434 *)
%t A274433 (* _Peter J. C. Moses_, Jun 17 2016 *)
%Y A274433 Cf. A000213, A274432, A274434.
%K A274433 nonn,easy
%O A274433 1,1
%A A274433 _Clark Kimberling_, Jun 22 2016