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

1, 3, 4, 7, 11, 12, 18, 21, 28, 29, 33, 44, 47, 54, 72, 76, 77, 84, 87, 116, 123, 126, 132, 141, 188, 198, 199, 203, 216, 228, 231, 304, 308, 319, 322, 329, 348, 369, 378, 492, 504, 517, 521, 522, 532, 564, 594, 597, 609, 792, 796, 812, 836, 843, 846, 861

Offset: 1

Author

Clark Kimberling, Jun 17 2016

Keywords

• nonn
• easy

Comments

See the Comment on distinct-product sequences in A160009.

Examples

			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,...
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000204, A160009, A274281 (includes 2).

Programs

Mathematica

f[1] = 1; f[2] = 3; z = 32; f[n_] := f[n - 1] + f[n - 2]; f = Table[f[n], {n, 1, z}]; f
s = {1}; Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}]; s
Take[Times@@@Subsets[LucasL[Range[20]]]//Union,60] (* Harvey P. Dale, Sep 26 2019 *)