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A274432
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Products of distinct tribonacci numbers (A000213).
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6
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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,...).
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MATHEMATICA
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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}];
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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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