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A054494
Largest Fibonacci factor of n.
7
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
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
KEYWORD
easy,nonn
AUTHOR
Henry Bottomley, Apr 04 2000
EXTENSIONS
Corrected by Harvey P. Dale, Jul 17 2012
STATUS
approved