A274281 - OEIS

%I #4 Jun 18 2016 00:39:39

%S 1,2,3,4,6,7,8,11,12,14,18,21,22,24,28,29,33,36,42,44,47,54,56,58,66,

%T 72,76,77,84,87,88,94,108,116,123,126,132,141,144,152,154,168,174,188,

%U 198,199,203,216,228,231,232,246,252,264,282,304,308,319,322

%N Numbers that are a product of distinct Lucas numbers (2,1,3,4,7,11,...)

%C See the Comment on distinct-product sequences in A160009.

%H Clark Kimberling, <a href="/A274281/b274281.txt">Table of n, a(n) for n = 1..1000</a>

%e The Lucas numbers are 2,1,3,4,7,11,18,29,..., so that the sequence of all products of distinct Lucas numbers, in increasing order, are 1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 18, 21, 22, 24, 28, 29,...

%t f[1] = 2; f[2] = 1; z = 32; f[n_] := f[n - 1] + f[n - 2]; f = Table[f[n], {n, 1, z}]; f

%t s = {1}; Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}]; s

%Y Cf. A160009, A274280.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jun 17 2016