The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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