

A201010


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


3



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
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OFFSET

1,2


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.


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


EXAMPLE

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


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[lim5], lim = lim+5]; f[lim] (* JeanFrançois Alcover, Jun 24 2015, after script by T. D. Noe in A200381 *)


CROSSREFS

Cf. A000032, A200381, A200995, A201011. Subsequence of A178772. Complement of A201012.
Sequence in context: A013939 A209921 A268377 * A004144 A124391 A200381
Adjacent sequences: A201007 A201008 A201009 * A201011 A201012 A201013


KEYWORD

nice,nonn


AUTHOR

Arkadiusz Wesolowski, Jan 08 2013


STATUS

approved



