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

Author

Carmine Suriano, Mar 02 2014

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

Cf. A000045, A080648.

Programs

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 *)

PARI

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

Formula

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