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A193615
Second-largest prime factor of the n-th Fibonacci number, if composite, or 1 otherwise.
4
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, 557, 47, 89, 1597, 13, 19, 149, 113, 233, 41, 2789, 211, 1, 199, 61, 461, 1, 47, 97, 151, 1597, 521, 953, 109, 661, 281, 797, 19489, 353, 61, 4513
OFFSET
3,4
COMMENTS
For clarification: if the largest prime factor occurs more than once, then that prime factor is selected.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 3..1422
EXAMPLE
F(82) = 2789 * 59369 * 370248451, so a(82) = 59369.
MATHEMATICA
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}]
PROG
(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])
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved