Numbers that are a product of distinct Lucas numbers (1,3,4,7,11,...)

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`%I #11 Jan 02 2024 16:14:03
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`%S 1,3,4,7,11,12,18,21,28,29,33,44,47,54,72,76,77,84,87,116,123,126,132,
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`%T 141,188,198,199,203,216,228,231,304,308,319,322,329,348,369,378,492,
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`%U 504,517,521,522,532,564,594,597,609,792,796,812,836,843,846,861
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`%N Numbers that are a product of distinct Lucas numbers (1,3,4,7,11,...)
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`%C See the Comment on distinct-product sequences in A160009.
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`%H Clark Kimberling, <a href="/A274280/b274280.txt">Table of n, a(n) for n = 1..1000</a>
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`%e The Lucas numbers are 1,3,4,7,11,18,29,..., so that the sequence of all products of distinct Lucas numbers, in increasing order, are 1, 3, 4, 7, 11, 12, 18, 21, 28, 29,...
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`%t f[1] = 1; f[2] = 3; z = 32; f[n_] := f[n - 1] + f[n - 2]; f = Table[f[n], {n, 1, z}]; f
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`%t s = {1}; Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}]; s
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`%t Take[Times@@@Subsets[LucasL[Range[20]]]//Union,60] (* _Harvey P. Dale_, Sep 26 2019 *)
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`%Y Cf. A000204, A160009, A274281 (includes 2).
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`%K nonn,easy
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`%O 1,2
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`%A _Clark Kimberling_, Jun 17 2016
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