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A274280 Numbers that are a product of distinct Lucas numbers (1,3,4,7,11,...)

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