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

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, 38, 41, 42, 44, 46, 47, 48, 49, 54, 56, 57, 58, 62, 63, 64, 66, 69, 72, 76, 77, 81, 82, 84, 87, 88, 92, 93, 94, 96, 98, 99, 107, 108, 112, 114, 116, 121, 123, 124, 126, 128

Offset: 1

Author

Arkadiusz Wesolowski, Jan 08 2013

Keywords

• nice
• nonn

Comments

These numbers do not occur in A178777.

The first 20 terms of this sequence are the same as in A004144 (nonhypotenuse numbers).

Integers of the form A200381(n)/A200381(m) for some m and n.

Examples

			19 is in the sequence because Lucas(9)/Lucas(0)^2 = 19.
		

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Lucas Number
• Index entries for Lucas sequences

Crossrefs

Cf. A000032, A200381, A200995, A201011. Subsequence of A178772. Complement of A201012.

Programs

Mathematica

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 *)