A193615 - OEIS

%I #20 Dec 09 2022 16:57:13

%S 1,1,1,2,1,3,2,5,1,3,1,13,5,7,1,17,37,11,13,89,1,7,5,233,53,29,1,31,

%T 557,47,89,1597,13,19,149,113,233,41,2789,211,1,199,61,461,1,47,97,

%U 151,1597,521,953,109,661,281,797,19489,353,61,4513

%N Second-largest prime factor of the n-th Fibonacci number, if composite, or 1 otherwise.

%C For clarification: if the largest prime factor occurs more than once, then that prime factor is selected.

%H Charles R Greathouse IV, <a href="/A193615/b193615.txt">Table of n, a(n) for n = 3..1422</a>

%e F(82) = 2789 * 59369 * 370248451, so a(82) = 59369.

%t factors[n_] := Flatten[Table[#[[1]], {#[[2]]}] & /@ FactorInteger[n]]; fn[n_] := Module[{fibn = Fibonacci[n]}, If[PrimeQ[fibn], 1, factors[fibn][[-2]]]]; Table[fn[n], {n, 3, 80}]

%o (PARI) a(n)=my(f=factor(fibonacci(n)),t=#f[,1]);if(f[t,2]==1,if(t==1,1,f[t-1,1]),f[t,1])

%Y Cf. A060385, A061488, A060442.

%K nonn

%O 3,4

%A _Charles R Greathouse IV_, Jul 31 2011