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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, 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
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
Sequence in context: A080648 A113195 A069110 * A352377 A202694 A123221
KEYWORD
nonn
AUTHOR
Carmine Suriano, Mar 02 2014
STATUS
approved