A274434 - OEIS

%I #4 Jun 22 2016 23:16:47

%S 135,255,459,465,765,837,855,1395,1539,1575,1581,2565,2635,2835,2895,

%T 2907,4725,4743,4845,5211,5301,5325,5355,8685,8721,8835,8925,9585,

%U 9765,9795,9843,15903,15975,16065,16275,16405,17631,17949,17955,18015,18105,29295

%N Products of three distinct tribonacci numbers > 1.

%C Are these unique among all products of distinct tribonacci numbers (A000213)?  (See A274432.)

%e The tribonacci numbers > 1 are 3,5,9,17,31,57,..., so that the trinary products in increasing order are 135, 255, 459, 465, 765,...

%t r[1] := 1; r[2] := 1; r[3] = 1; r[n_] := r[n] = r[n - 1] + r[n - 2] + r[n - 3];

%t s = {1}; z = 60; f = Map[r, Range[z]]; Take[f, 20]

%t Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}];

%t Take[s, 2 z]  (* A274432 *)

%t infQ[n_] := MemberQ[f, n];

%t ans = Table[#[[Flatten[Position[Map[Apply[Times, #] &, #], s[[n]]]][[1]]]] &[

%t Rest[Subsets[Map[#[[1]] &, Select[Map[{#, infQ[#]} &, Divisors[s[[n]]]], #[[2]] && #[[1]] > 1 &]]]]], {n, 2, 300}];

%t Map[Apply[Times, #] &, Select[ans, Length[#] == 2 &]] (* A274433 *)

%t Map[Apply[Times, #] &, Select[ans, Length[#] == 3 &]] (* A274434 *)

%t (* _Peter J. C. Moses_, Jun 17 2016 *)

%Y Cf. A000213, A274432, A274433.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jun 22 2016