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A274432 Products of distinct tribonacci numbers (A000213). 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

EXAMPLE

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,...).

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 *)

CROSSREFS

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

Sequence in context: A111249 A190804 A100812 * A190939 A018634 A310041

Adjacent sequences:  A274429 A274430 A274431 * A274433 A274434 A274435

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 22 2016

STATUS

approved

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Last modified January 23 16:48 EST 2020. Contains 331173 sequences. (Running on oeis4.)