A135939 Highest exponent occurring in the prime factorization of Fibonacci(n).

1, 1, 1, 3, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 5, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 6, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 5, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 7, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1

Offset: 3

Author

Colm Mulcahy, Mar 04 2008

Keywords

• nonn

Examples

			a(12) = 4 since Fibonacci(12) = 144 = 2^4 * 3^2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 3..1422

Crossrefs

Cf. A000045, A051903.

Programs

Maple

A051903 := proc(n) if n = 1 then 0 ; else max(seq(op(2,i),i=ifactors(n)[2])) ; fi ; end: A135939 := proc(n) A051903(combinat[fibonacci](n)) ; end: seq(A135939(n),n=3..120) ; # R. J. Mathar, Mar 16 2008

Mathematica

f[n_]:=Max[Last/@FactorInteger[n]];Table[f[Fibonacci[n]],{n,3,5!}] (* Vladimir Joseph Stephan Orlovsky, Apr 10 2010 *)

PARI

for(n=3,200,print1(vecmax(factor(fibonacci(n))[,2])",")) \\ Yolinda (yoliahmed33(AT)yandex.ru), Mar 27 2008

Formula

a(n) = A051903(A000045(n)). - Amiram Eldar, Sep 09 2024

Extensions

More terms from R. J. Mathar and Yolinda (yoliahmed33(AT)yandex.ru), Mar 16 2008