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A201010 Integers that can be written as the product and/or quotient of Lucas numbers.

%I A201010 #28 Feb 16 2025 08:33:16
%S A201010 1,2,3,4,6,7,8,9,11,12,14,16,18,19,21,22,23,24,27,28,29,31,32,33,36,
%T A201010 38,41,42,44,46,47,48,49,54,56,57,58,62,63,64,66,69,72,76,77,81,82,84,
%U A201010 87,88,92,93,94,96,98,99,107,108,112,114,116,121,123,124,126,128
%N A201010 Integers that can be written as the product and/or quotient of Lucas numbers.
%C A201010 These numbers do not occur in A178777.
%C A201010 The first 20 terms of this sequence are the same as in A004144 (nonhypotenuse numbers).
%C A201010 Integers of the form A200381(n)/A200381(m) for some m and n.
%H A201010 Arkadiusz Wesolowski, <a href="/A201010/b201010.txt">Table of n, a(n) for n = 1..10000</a>
%H A201010 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LucasNumber.html">Lucas Number</a>
%H A201010 <a href="/index/Lu#Lucas">Index entries for Lucas sequences</a>
%e A201010 19 is in the sequence because Lucas(9)/Lucas(0)^2 = 19.
%t A201010 maxTerm = 128; Clear[f]; f[lim_] := f[lim] = (luc = LucasL[Range[0, lim]]; luc = Delete[luc, 2];  last = luc[[-1]]; t = {1}; Do[t2 = luc[[n]]^Range[ Floor[ Log[last] / Log[ luc[[n]] ]]]; s = Select[ Union[ Flatten[ Outer[ Times, t, t2]]], # <= last &]; t = Union[t, s], {n, lim}]; maxIndex = Length[A200381 = t]; Reap[ Do[r = A200381[[n]] / A200381[[m]]; If[IntegerQ[r] && r <= maxTerm, Sow[r]], {n, 1, maxIndex}, {m, 1, maxIndex}]][[2, 1]] // Union); f[5]; f[lim = 10]; While[ Print["lim = ", lim]; f[lim] != f[lim-5], lim = lim+5]; f[lim] (* _Jean-François Alcover_, Jun 24 2015, after script by _T. D. Noe_ in A200381 *)
%Y A201010 Cf. A000032, A200381, A200995, A201011. Subsequence of A178772. Complement of A201012.
%K A201010 nice,nonn
%O A201010 1,2
%A A201010 _Arkadiusz Wesolowski_, Jan 08 2013