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A287677
Practical Lucas numbers.
2
1, 4, 18, 5778, 215002084978043708894524818, 8000328475168735073037785452636987975637751878418, 267093222236137978360266538108484045754096036229865700498, 8916982544642128998138920801180413422215946187628307595501392018
OFFSET
1,2
COMMENTS
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 ...
LINKS
Giuseppe Melfi, A survey on practical numbers, Rend. Sem. Mat. Univ. Pol. Torino, 53, (1995), 347-359.
EXAMPLE
18 is in this sequence since it is the 6th Lucas number, A000032(6) and it is also a practical number, A005153(8).
MATHEMATICA
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]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 29 2017
STATUS
approved