A105602 Divide each Fibonacci number by its primitive part.

1, 1, 1, 1, 1, 2, 1, 3, 2, 5, 1, 24, 1, 13, 10, 21, 1, 136, 1, 165, 26, 89, 1, 1008, 5, 233, 34, 1131, 1, 26840, 1, 987, 178, 1597, 65, 46512, 1, 4181, 466, 47355, 1, 1269736, 1, 53133, 10370, 28657, 1, 2179296, 13, 825275, 3194, 364179, 1, 14927768, 445

Offset: 1

Author

Paul Barry, Apr 15 2005

Keywords

• easy
• nonn

Comments

Sylvester dividends for Fibonacci numbers.

a(n)=1 for n=1, 4 and all primes, which is sequence A046022.

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A000045, A046022, A061446, A126015.

Programs

Mathematica

a[n_] := Fibonacci[n]/Product[Fibonacci[d]^MoebiusMu[n/d], {d, Divisors[n]}]; Table[a[n],{n,55}] (* James C. McMahon, Jan 25 2024 *)

Formula

a(n) = Fibonacci(n)/A061446(n).