A274432 Products of distinct tribonacci numbers (A000213).

3, 5, 9, 15, 17, 27, 31, 45, 51, 57, 85, 93, 105, 135, 153, 155, 171, 193, 255, 279, 285, 315, 355, 459, 465, 513, 525, 527, 579, 653, 765, 837, 855, 945, 965, 969, 1065, 1201, 1395, 1539, 1575, 1581, 1737, 1767, 1775, 1785, 1959, 2209, 2295, 2565, 2635

Offset: 1

Author

Clark Kimberling, Jun 22 2016

Keywords

• nonn
• easy

Examples

			The tribonacci numbers are 1,1,1,3,5,9,17,31,..., so that the sequence of all products of distinct members, in increasing order, is (3, 5, 9, 15, 17, 27, 31, 45,...).
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A160009, A274280, A274433 (binary products), A274434 (trinary products).

Programs

Mathematica

r[1] := 1; r[2] := 1; r[3] = 1; r[n_] := r[n] = r[n - 1] + r[n - 2] + r[n - 3];
s = {1}; z = 60; f = Map[r, Range[z]]; Take[f, 20]
Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}];
Take[s, 2 z]  (*A274432*)
infQ[n_] := MemberQ[f, n];
ans = Table[#[[Flatten[Position[Map[Apply[Times, #] &, #], s[[n]]]][[1]]]] &[
Rest[Subsets[Map[#[[1]] &, Select[Map[{#, infQ[#]} &, Divisors[s[[n]]]], #[[2]] && #[[1]] > 1 &]]]]], {n, 2, 300}];
Map[Apply[Times, #] &, Select[ans, Length[#] == 2 &]] (* A274433 *)
Map[Apply[Times, #] &, Select[ans, Length[#] == 3 &]] (* A274434 *)
(* Peter J. C. Moses, Jun 17 2016 *)