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A287677
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Practical Lucas numbers.
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2
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1, 4, 18, 5778, 215002084978043708894524818, 8000328475168735073037785452636987975637751878418, 267093222236137978360266538108484045754096036229865700498, 8916982544642128998138920801180413422215946187628307595501392018
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OFFSET
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1,2
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COMMENTS
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Melfi proved that this sequence is infinite.
The indices of these Lucas numbers are 1, 3, 6, 18, 126, 234, 270, 306, 342, 378, 450, 522 ...
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LINKS
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EXAMPLE
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18 is in this sequence since it is the 6th Lucas number, A000032(6) and it is also a practical number, A005153(8).
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MATHEMATICA
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PracticalQ[n_] := Module[{f, p, e, prod=1, ok=True}, If[n<1 || (n>1 && OddQ[n]), False, If[n==1, True, f=FactorInteger[n]; {p, e} = Transpose[f]; Do[If[p[[i]] > 1+DivisorSigma[1, prod], ok=False; Break[]]; prod=prod*p[[i]]^e[[i]], {i, Length[p]}]; ok]]]; Select[Table[LucasL[n], {n, 1, 310}], PracticalQ]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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