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A115022 a(n) = F(n-th squarefree)/product{p=primes,p|(n-th squarefree)} F(p), where F(m) is m-th Fibonacci number.

%I A115022 #17 Dec 05 2018 04:00:36
%S A115022 1,1,1,1,4,1,11,1,1,29,61,1,1,421,199,1,521,1,83204,1,19801,3571,
%T A115022 141961,1,9349,135721,1,10304396,1,64079,1,6376021,1,313671601,
%U A115022 43701901,1149851,1,1,3010349,14736206161,156055561996,1,2053059121
%N A115022 a(n) = F(n-th squarefree)/product{p=primes,p|(n-th squarefree)} F(p), where F(m) is m-th Fibonacci number.
%H A115022 Robert Israel, <a href="/A115022/b115022.txt">Table of n, a(n) for n = 1..2938</a>
%e A115022 The 7th squarefree integer is 10 = 2*5. So a(7) = F(10)/(F(2)F(5)) = 55/(1*5) = 11.
%p A115022 count:= 0:
%p A115022 for n from 1 while count < 50 do
%p A115022   if numtheory:-issqrfree(n) then
%p A115022      count:= count+1;
%p A115022      A[count]:= combinat:-fibonacci(n)/mul(combinat:-fibonacci(p),p=numtheory:-factorset(n))
%p A115022   fi
%p A115022 od:
%p A115022 seq(A[i],i=1..50); # _Robert Israel_, Dec 04 2018
%t A115022 f[n_] := Fibonacci[n]/Times @@ (Fibonacci /@ FactorInteger[n][[;; , 1]]); f /@
%t A115022 Select[Range[70], SquareFreeQ[#] &] (* _Amiram Eldar_, Dec 04 2018 *)
%Y A115022 Cf. A075731.
%Y A115022 a(n)=1 if n is in A071403.
%K A115022 nonn,look
%O A115022 1,5
%A A115022 _Leroy Quet_, Feb 28 2006
%E A115022 More terms from _Joshua Zucker_, Jul 18 2007