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

1,5

Links

Robert Israel, Table of n, a(n) for n = 1..2938

Example

The 7th squarefree integer is 10 = 2*5. So a(7) = F(10)/(F(2)F(5)) = 55/(1*5) = 11.

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 *)

Crossrefs

Cf. A075731.

a(n)=1 if n is in A071403.

Sequence in context: A283433 A121463 A244608 * A230534 A177822 A091156

Adjacent sequences: A115019 A115020 A115021 * A115023 A115024 A115025

Keyword

nonn,look

Author

Leroy Quet, Feb 28 2006

Extensions

More terms from Joshua Zucker, Jul 18 2007

Status

approved