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A287677 Practical Lucas numbers. 2
1, 4, 18, 5778, 215002084978043708894524818, 8000328475168735073037785452636987975637751878418, 267093222236137978360266538108484045754096036229865700498, 8916982544642128998138920801180413422215946187628307595501392018 (list; graph; refs; listen; history; text; internal format)
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

Amiram Eldar, Table of n, a(n) for n = 1..12

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

Cf. A000032, A005153, A124105, A287679.

Sequence in context: A173222 A156491 A342467 * A069874 A222323 A012496

Adjacent sequences:  A287674 A287675 A287676 * A287678 A287679 A287680

KEYWORD

nonn

AUTHOR

Amiram Eldar, May 29 2017

STATUS

approved

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Last modified January 21 12:13 EST 2022. Contains 350477 sequences. (Running on oeis4.)