OFFSET
1,3
COMMENTS
These are Fibonacci numbers of order 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, and 48. It is somewhat surprising that these are only these Fibonacci numbers having this property.
LINKS
Florian Luca and Lawrence Somer, Lucas sequences for which 4 | phi(abs(u_n)) for almost all n, Fibonacci Quarterly, 44 (2006), pp. 249-262.
MATHEMATICA
Join[{1, 1}, Select[Fibonacci[Range[200]], Union[Mod[Transpose[FactorInteger[#]][[1]], 4]][[1]] > 1 &]]
npfQ[n_]:=Count[FactorInteger[n][[All, 1]], _?(Mod[#, 4]==1&)]==0; Join[ {1, 1}, Select[ Fibonacci[Range[50]], npfQ]] (* Harvey P. Dale, Jun 15 2019 *)
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
T. D. Noe, Feb 26 2014
STATUS
approved