A139044 Smallest prime divisor of the Fibonacci numbers > 1.

2, 3, 5, 2, 13, 3, 2, 5, 89, 2, 233, 13, 2, 3, 1597, 2, 37, 3, 2, 89, 28657, 2, 5, 233, 2, 3, 514229, 2, 557, 3, 2, 1597, 5, 2, 73, 37, 2, 3, 2789, 2, 433494437, 3, 2, 139, 2971215073, 2, 13, 5, 2, 3, 953, 2, 5, 3, 2, 59, 353, 2, 4513, 557, 2, 3, 5, 2, 269, 3, 2, 5, 6673, 2

Offset: 1

Author

Omar E. Pol, Apr 23 2008

Keywords

• nonn

Comments

Fibonacci number > 1, divided by its largest proper divisor.

Links

• Tyler Busby, Table of n, a(n) for n = 1..1450 (terms 1..200 Vincenzo Librandi, terms 201..1406 from Amiram Eldar)

Crossrefs

Cf. A000045, A032742, A060383, A133021, A139045.

Programs

Magma

[Minimum(PrimeDivisors(Fibonacci(n+2))): n in [1..70]]; // Vincenzo Librandi, Dec 24 2016

Maple

with(numtheory): with(combinat): a:=proc(n) options operator, arrow: op(2, divisors(fibonacci(n))) end proc: seq(a(n),n=3..60); # Emeric Deutsch, May 02 2008

Mathematica

First[First[FactorInteger[ # ]]]&/@Fibonacci[Range[3,40]] (* Harvey P. Dale, Apr 30 2008 *)

PARI

a(n) = factor(fibonacci(n+2))[1,1]; \\ Michel Marcus, Nov 15 2014

Formula

a(n) = A000045(n+2)/A032742(A000045(n+2)) = A000045(n+2)/A139045(n).

a(n) = A020639(A000045(n+2)). - Michel Marcus, Nov 15 2014

a(n) = A060383(n+2). - Alois P. Heinz, Oct 11 2015

Extensions

More terms from Emeric Deutsch and Harvey P. Dale, May 02 2008

More terms from Vincenzo Librandi, Dec 24 2016