A280699 -id:A280699 - 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)

A280694 Largest Lucas number (A000032) dividing n.

Original entry on oeis.org

1, 2, 3, 4, 1, 3, 7, 4, 3, 2, 11, 4, 1, 7, 3, 4, 1, 18, 1, 4, 7, 11, 1, 4, 1, 2, 3, 7, 29, 3, 1, 4, 11, 2, 7, 18, 1, 2, 3, 4, 1, 7, 1, 11, 3, 2, 47, 4, 7, 2, 3, 4, 1, 18, 11, 7, 3, 29, 1, 4, 1, 2, 7, 4, 1, 11, 1, 4, 3, 7, 1, 18, 1, 2, 3, 76, 11, 3, 1, 4, 3, 2, 1, 7, 1, 2, 29, 11, 1, 18, 7, 4, 3, 47, 1, 4, 1, 7, 11, 4, 1, 3, 1, 4, 7, 2, 1, 18, 1, 11, 3, 7, 1

Offset: 1

Antti Karttunen, Jan 11 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..15127

Cf. A000032, A054494, A280695, A280699.

Cf. A057854 (gives the positions n > 1 where this sequence and A280696 obtain equal values).

;; A stand-alone program:
(define (A280694 n) (let loop ((l1 1) (l2 3) (lpd 1)) (cond ((> l1 n) (if (and (= 1 lpd) (even? n)) 2 lpd)) ((zero? (modulo n l1)) (loop l2 (+ l1 l2) l1)) (else (loop l2 (+ l1 l2) lpd)))))

a(n) = n / A280695(n).
Other identities. For all n >= 1:
a(A000032(n)) = A000032(n).
a(A057854(n)) = A280696(A057854(n)).
a(A000045(n)) = A280699(n).

A280696 Largest Lucas proper divisor of n, a(1) = a(2) = 1.

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 1, 4, 3, 2, 1, 4, 1, 7, 3, 4, 1, 3, 1, 4, 7, 11, 1, 4, 1, 2, 3, 7, 1, 3, 1, 4, 11, 2, 7, 18, 1, 2, 3, 4, 1, 7, 1, 11, 3, 2, 1, 4, 7, 2, 3, 4, 1, 18, 11, 7, 3, 29, 1, 4, 1, 2, 7, 4, 1, 11, 1, 4, 3, 7, 1, 18, 1, 2, 3, 4, 11, 3, 1, 4, 3, 2, 1, 7, 1, 2, 29, 11, 1, 18, 7, 4, 3, 47, 1, 4, 1, 7, 11, 4, 1, 3, 1, 4, 7, 2, 1, 18, 1, 11, 3, 7, 1, 3, 1

Offset: 1

Antti Karttunen, Jan 11 2017

nonn

For n > 1, a(n) = greatest Lucas number (A000032) that divides n and is less than n.

Antti Karttunen, Table of n, a(n) for n = 1..15127

Cf. A000032, A000045, A000204, A280686, A280697, A280698, A280699.

Cf. A057854 (gives the positions n > 1 where this sequence and A280694 obtain equal values).

;; A stand-alone program:
(define (A280696 n) (let loop ((l1 1) (l2 3) (lpd 1)) (cond ((>= l1 n) (if (and (= 1 lpd) (even? n) (> n 2)) 2 lpd)) ((zero? (modulo n l1)) (loop l2 (+ l1 l2) l1)) (else (loop l2 (+ l1 l2) lpd)))))

a(n) = n / A280697(n).
Other identities. For all n >= 1:
a(A057854(n)) = A280694(A057854(n)).
a(A000204(n)) = A280698(n).

A280698 Greatest Lucas number that is a proper divisor of the n-th Lucas number, a(1) = 1.

Original entry on oeis.org

1, 1, 2, 1, 1, 3, 1, 1, 4, 3, 1, 7, 1, 3, 11, 1, 1, 18, 1, 7, 29, 3, 1, 47, 11, 3, 76, 7, 1, 123, 1, 1, 199, 3, 29, 322, 1, 3, 521, 47, 1, 843, 1, 7, 1364, 3, 1, 2207, 29, 123, 3571, 7, 1, 5778, 199, 47, 9349, 3, 1, 15127, 1, 3, 24476, 1, 521, 39603, 1, 7, 64079, 843, 1, 103682, 1, 3, 167761, 7, 199, 271443, 1, 2207, 439204, 3, 1, 710647, 3571, 3, 1149851, 47, 1

Offset: 1

Antti Karttunen, Jan 11 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..521

Cf. A000032, A000204, A105800, A280696, A280699.

(define (A280698 n) (A280696 (A000204 n)))

a(n) = A280696(A000204(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.

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A280694 Largest Lucas number (A000032) dividing n.

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A280696 Largest Lucas proper divisor of n, a(1) = a(2) = 1.

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A280698 Greatest Lucas number that is a proper divisor of the n-th Lucas number, a(1) = 1.

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