A238684 a(1) = a(2) = 1; for n > 2, a(n) is the product of prime factors of the n-th Fibonacci number.

1, 1, 2, 3, 5, 2, 13, 21, 34, 55, 89, 6, 233, 377, 610, 987, 1597, 646, 4181, 6765, 10946, 17711, 28657, 966, 15005, 121393, 196418, 317811, 514229, 208010, 1346269, 2178309, 3524578, 5702887, 9227465, 207366, 24157817, 39088169, 63245986, 102334155, 165580141, 66978574, 433494437, 701408733, 1134903170

Offset

1,3

Comments

In other words, the squarefree part of the n-th Fibonacci number.

a(gcd(m,n)) = gcd(a(m),a(n)). - Robert Israel, Nov 10 2023

Links

Robert Israel, Table of n, a(n) for n = 1..350

Formula

a(n) = A007947(A000045(n)) - Tom Edgar, Mar 03 2014

Example

a(12) = 6 since F(12) = 144 = 2^4 * 3^2 and 2 * 3 = 6.

Maple

f:= n -> convert(numtheory:-factorset(combinat:-fibonacci(n)), `*`):
map(f, [$1..100]); # Robert Israel, Nov 10 2023

Mathematica

Table[Times@@Part[Flatten[FactorInteger[Fibonacci[n]]], 1 ;; -2 ;; 2], {n, 3, 50}] (* Alonso del Arte, Mar 02 2014 *)

Prog

(PARI) a(n) = my(f = factor(fibonacci(n))); prod(i=1, #f~, f[i, 1]); \\ Michel Marcus, Mar 02 2014

Crossrefs

Cf. A000045, A080648.

Sequence in context: A080648 A113195 A069110 * A352377 A202694 A123221

Adjacent sequences: A238681 A238682 A238683 * A238685 A238686 A238687

Keyword

nonn

Author

Carmine Suriano, Mar 02 2014

Status

approved