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
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