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Divide each Fibonacci number by its primitive part.
4

%I #13 Jan 25 2024 11:44:06

%S 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,

%T 34,1131,1,26840,1,987,178,1597,65,46512,1,4181,466,47355,1,1269736,1,

%U 53133,10370,28657,1,2179296,13,825275,3194,364179,1,14927768,445

%N Divide each Fibonacci number by its primitive part.

%C Sylvester dividends for Fibonacci numbers.

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

%H T. D. Noe, <a href="/A105602/b105602.txt">Table of n, a(n) for n=1..1000</a>

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

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

%Y Cf. A000045, A046022, A061446, A126015.

%K easy,nonn

%O 1,6

%A _Paul Barry_, Apr 15 2005