A280690 -id:A280690 - cp's OEIS frontend

A105800 Greatest Fibonacci number that is a proper divisor of the n-th Fibonacci number; a(1) = a(2) = 1.

1, 1, 1, 1, 1, 2, 1, 3, 2, 5, 1, 8, 1, 13, 5, 21, 1, 34, 1, 55, 13, 89, 1, 144, 5, 233, 34, 377, 1, 610, 1, 987, 89, 1597, 13, 2584, 1, 4181, 233, 6765, 1, 10946, 1, 17711, 610, 28657, 1, 46368, 13, 75025, 1597, 121393, 1, 196418, 89, 317811, 4181, 514229, 1, 832040, 1

Offset: 1

Reinhard Zumkeller, Apr 20 2005

nonn

a(A001605(n)) = 1.

Antti Karttunen, Table of n, a(n) for n = 1..987
Eric Weisstein's World of Mathematics, Fibonacci Number
Wikipedia, Divisibility sequence

Cf. A000045, A032742, A076984, A139045, A280686, A280688, A280689, A280690, A280698, A280699.

Cf. A046022 (gives the positions of ones).

nn=70;Join[{1,1},With[{fibs=Fibonacci[Range[nn]]},Table[ Max[ Intersection[ Most[Divisors[fibs[[n]]]],fibs]],{n,3,nn}]]] (* Harvey P. Dale, Apr 10 2012 *)

From Antti Karttunen, Jan 11 2017: (Start)
a(n) = A280686(A000045(n)).
a(n) = A000045(A032742(n)). [Because A000045 is a divisibility sequence.]
a(A032742(n)) = A280688(n).
(End)

A280689 a(n) = A000045(A032742(n)) / A000045(A054576(n)), where A000045(n) gives the n-th Fibonacci number, A032742(n) = the largest proper divisor of n, and A054576(n) = A032742(A032742(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 3, 2, 5, 1, 4, 1, 13, 5, 7, 1, 17, 1, 11, 13, 89, 1, 18, 5, 233, 17, 29, 1, 122, 1, 47, 89, 1597, 13, 76, 1, 4181, 233, 123, 1, 842, 1, 199, 122, 28657, 1, 322, 13, 15005, 1597, 521, 1, 5777, 89, 843, 4181, 514229, 1, 1364, 1, 1346269, 842, 2207, 233, 39602, 1, 3571, 28657, 709805, 1, 5778, 1, 24157817, 15005, 9349, 89, 271442, 1, 15127, 5777

Offset: 1

Antti Karttunen, Jan 11 2017

nonn

A000045 is a divisibility sequence, which guarantees that the result of the division is an integer.

Antti Karttunen, Table of n, a(n) for n = 1..987
Wikipedia, Divisibility sequence

Cf. A000045, A032742, A054576, A105800, A280688, A280690, A280691.

(define (A280689 n) (/ (A105800 n) (A280688 n)))

a(n) = A105800(n) / A280688(n) = A105800(n) / A105800(A032742(n)).
a(n) = A000045(A032742(n)) / A000045(A054576(n)).
a(n) = A280690(A032742(n)).

A280687 a(n) = n / A280686(n); n divided by its largest Fibonacci proper divisor, a(1) = 1.

Original entry on oeis.org

1, 2, 3, 2, 5, 2, 7, 4, 3, 2, 11, 4, 13, 7, 3, 2, 17, 6, 19, 4, 7, 11, 23, 3, 5, 2, 9, 14, 29, 6, 31, 4, 11, 17, 7, 12, 37, 19, 3, 5, 41, 2, 43, 22, 9, 23, 47, 6, 49, 10, 17, 4, 53, 18, 11, 7, 19, 29, 59, 12, 61, 31, 3, 8, 5, 22, 67, 2, 23, 14, 71, 9, 73, 37, 15, 38, 77, 6, 79, 10, 27, 41, 83, 4, 17, 43, 29, 11, 89, 18, 7, 46, 31, 47, 19, 12, 97, 49, 33, 20

Offset: 1

Antti Karttunen, Jan 11 2017

nonn

For n > 1, a(n) = n divided by the greatest Fibonacci number that divides n and is less than n.

Antti Karttunen, Table of n, a(n) for n = 1..10946

Cf. A000045, A280686, A280690, A280697.

Scheme
```
(define (A280687 n) (/ n (A280686 n)))
```

a(n) = n / A280686(n).

a(A000045(n)) = A280690(n).

cp's OEIS Frontend

A105800 Greatest Fibonacci number that is a proper divisor of the n-th Fibonacci number; a(1) = a(2) = 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A280689 a(n) = A000045(A032742(n)) / A000045(A054576(n)), where A000045(n) gives the n-th Fibonacci number, A032742(n) = the largest proper divisor of n, and A054576(n) = A032742(A032742(n)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Scheme

Formula

A280687 a(n) = n / A280686(n); n divided by its largest Fibonacci proper divisor, a(1) = 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Scheme

Formula