A193615 Second-largest prime factor of the n-th Fibonacci number, if composite, or 1 otherwise.

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

Cf. A060385, A061488, A060442.

Sequence in context: A215489 A182167 A117364 * A300383 A120250 A280689

Adjacent sequences: A193612 A193613 A193614 * A193616 A193617 A193618

Keyword

nonn

Author

Charles R Greathouse IV, Jul 31 2011

Status

approved