cp's OEIS Frontend

A139045 Largest proper divisor of the Fibonacci numbers > 1.

%I A139045 #21 Nov 05 2019 19:53:19
%S A139045 1,1,1,4,1,7,17,11,1,72,1,29,305,329,1,1292,113,2255,5473,199,1,23184,
%T A139045 15005,521,98209,105937,1,416020,2417,726103,1762289,3571,1845493,
%U A139045 7465176,330929,1056437,31622993,34111385,59369,133957148,1,233802911,567451585
%N A139045 Largest proper divisor of the Fibonacci numbers > 1.
%C A139045 See the list of divisors of positive Fibonacci numbers in the triangle A133021.
%C A139045 See the largest proper divisor of n in A032742.
%C A139045 Fibonacci(1)=Fibonacci(2)=1 do not have proper divisors. - _Emeric Deutsch_, May 18 2008
%H A139045 Amiram Eldar, <a href="/A139045/b139045.txt">Table of n, a(n) for n = 3..1000</a>
%F A139045 a(n) = A032742(A000045(n)).
%F A139045 a(n) = A000045(n)/A060383(n). - _Alois P. Heinz_, Sep 03 2019
%e A139045 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 A139045 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 A139045 # second Maple program:
%p A139045 a:= n-> (f-> f/min(numtheory[factorset](f)))((<<0|1>, <1|1>>^n)[1, 2]):
%p A139045 seq(a(n), n=3..47);  # _Alois P. Heinz_, Sep 03 2019
%t A139045 lpd[n_]:=Divisors[n][[-2]]; lpd/@(Fibonacci[Range[3,40]]) (* _Harvey P. Dale_, Mar 29 2015 *)
%Y A139045 Cf. A000045, A032742, A060383, A133021, A133028, A134708.
%K A139045 nonn
%O A139045 3,4
%A A139045 _Omar E. Pol_, Apr 23 2008
%E A139045 More terms from _Emeric Deutsch_, May 18 2008