A105602 - OEIS

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

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OFFSET

1,6

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

FORMULA

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

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 *)