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%I #11 Feb 18 2021 00:45:44
%S 1,1,2,3,8,21,144,987,46368,2178309,4807526976
%N Fibonacci numbers that have no prime factors of the form 4k+1.
%C 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.
%H Florian Luca and Lawrence Somer, <a href="http://www.fq.math.ca/44-3.html">Lucas sequences for which 4 | phi(abs(u_n)) for almost all n</a>, Fibonacci Quarterly, 44 (2006), pp. 249-262.
%t Join[{1, 1}, Select[Fibonacci[Range[200]], Union[Mod[Transpose[FactorInteger[#]][[1]], 4]][[1]] > 1 &]]
%t 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 *)
%Y Cf. A000045 (Fibonacci numbers).
%K nonn,fini,full
%O 1,3
%A _T. D. Noe_, Feb 26 2014
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