A139045 - OEIS

%I #21 Nov 05 2019 19:53:19

%S 1,1,1,4,1,7,17,11,1,72,1,29,305,329,1,1292,113,2255,5473,199,1,23184,

%T 15005,521,98209,105937,1,416020,2417,726103,1762289,3571,1845493,

%U 7465176,330929,1056437,31622993,34111385,59369,133957148,1,233802911,567451585

%N Largest proper divisor of the Fibonacci numbers > 1.

%C See the list of divisors of positive Fibonacci numbers in the triangle A133021.

%C See the largest proper divisor of n in A032742.

%C Fibonacci(1)=Fibonacci(2)=1 do not have proper divisors. - _Emeric Deutsch_, May 18 2008

%H Amiram Eldar, <a href="/A139045/b139045.txt">Table of n, a(n) for n = 3..1000</a>

%F a(n) = A032742(A000045(n)).

%F a(n) = A000045(n)/A060383(n). - _Alois P. Heinz_, Sep 03 2019

%e a(9) = 17 because the 9th Fibonacci number is 34 and the divisors of 34 are 1, 2, 17, 34, then the largest proper divisor of 34 is 17.

%p with(combinat): with(numtheory): a:=proc(n) options operator, arrow: op(tau(fibonacci(n))-1, divisors(fibonacci(n))) end proc: seq(a(n),n=3..40); # _Emeric Deutsch_, May 18 2008

%p # second Maple program:

%p a:= n-> (f-> f/min(numtheory[factorset](f)))((<<0|1>, <1|1>>^n)[1, 2]):

%p seq(a(n), n=3..47);  # _Alois P. Heinz_, Sep 03 2019

%t lpd[n_]:=Divisors[n][[-2]]; lpd/@(Fibonacci[Range[3,40]]) (* _Harvey P. Dale_, Mar 29 2015 *)

%Y Cf. A000045, A032742, A060383, A133021, A133028, A134708.

%K nonn

%O 3,4

%A _Omar E. Pol_, Apr 23 2008

%E More terms from _Emeric Deutsch_, May 18 2008