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

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

Author

Antti Karttunen, Jan 11 2017

Keywords

• nonn

Comments

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

Links

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

Crossrefs

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

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

Programs

Scheme

;; 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)))))

Formula

a(n) = n / A280697(n).

Other identities. For all n >= 1:

a(A057854(n)) = A280694(A057854(n)).

a(A000204(n)) = A280698(n).