A115022 a(n) = F(n-th squarefree)/product{p=primes,p|(n-th squarefree)} F(p), where F(m) is m-th Fibonacci number.
1, 1, 1, 1, 4, 1, 11, 1, 1, 29, 61, 1, 1, 421, 199, 1, 521, 1, 83204, 1, 19801, 3571, 141961, 1, 9349, 135721, 1, 10304396, 1, 64079, 1, 6376021, 1, 313671601, 43701901, 1149851, 1, 1, 3010349, 14736206161, 156055561996, 1, 2053059121
Offset: 1
Examples
The 7th squarefree integer is 10 = 2*5. So a(7) = F(10)/(F(2)F(5)) = 55/(1*5) = 11.
Links
- Robert Israel, Table of n, a(n) for n = 1..2938
Programs
-
Maple
count:= 0: for n from 1 while count < 50 do if numtheory:-issqrfree(n) then count:= count+1; A[count]:= combinat:-fibonacci(n)/mul(combinat:-fibonacci(p),p=numtheory:-factorset(n)) fi od: seq(A[i],i=1..50); # Robert Israel, Dec 04 2018 -
Mathematica
f[n_] := Fibonacci[n]/Times @@ (Fibonacci /@ FactorInteger[n][[;; , 1]]); f /@ Select[Range[70], SquareFreeQ[#] &] (* Amiram Eldar, Dec 04 2018 *)
Extensions
More terms from Joshua Zucker, Jul 18 2007