A054494 Largest Fibonacci factor of n.

1, 2, 3, 2, 5, 3, 1, 8, 3, 5, 1, 3, 13, 2, 5, 8, 1, 3, 1, 5, 21, 2, 1, 8, 5, 13, 3, 2, 1, 5, 1, 8, 3, 34, 5, 3, 1, 2, 13, 8, 1, 21, 1, 2, 5, 2, 1, 8, 1, 5, 3, 13, 1, 3, 55, 8, 3, 2, 1, 5, 1, 2, 21, 8, 13, 3, 1, 34, 3, 5, 1, 8, 1, 2, 5, 2, 1, 13, 1, 8, 3, 2, 1, 21, 5, 2, 3, 8, 89, 5, 13, 2, 3, 2, 5, 8, 1, 2, 3, 5

Offset

1,2

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) = n/A054495(n).

Example

a(10)=5 because 1, 2 and 5 are the Fibonacci numbers which divide 10 and 5 is the largest.

Mathematica

With[{fibs=Fibonacci[Range[20]]}, Table[Max[Select[fibs, Divisible[ n, #]&]], {n, 100}]] (* Harvey P. Dale, Jul 17 2012 *)

Prog

(PARI) A010056(n)=my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8))
a(n)=fordiv(n, d, if(A010056(n/d), return(n/d))) \\ Charles R Greathouse IV, Nov 05 2014
(Python)
from sympy import divisors
from sympy.ntheory.primetest import is_square
def A054494(n): return next(d for d in sorted(divisors(n, generator=True), reverse=True) if is_square(m:=5*d**2-4) or is_square(m+8)) # Chai Wah Wu, May 06 2024

Crossrefs

Cf. A000045, A005086, A010056, A054495.

Sequences with similar definitions: A047930 (smallest Fibonacci multiple), A280686 (restricted to proper divisors), A280694 (equivalent for Lucas numbers).

Positions of 1's: A147956.

Sequence in context: A174621 A369029 A007967 * A306252 A112764 A108728

Adjacent sequences: A054491 A054492 A054493 * A054495 A054496 A054497

Keyword

easy,nonn

Author

Henry Bottomley, Apr 04 2000

Extensions

Corrected by Harvey P. Dale, Jul 17 2012

Status

approved