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Largest Lucas number (A000032) dividing n.
5

%I #12 Jan 12 2017 07:18:45

%S 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,

%T 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,

%U 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

%N Largest Lucas number (A000032) dividing n.

%H Antti Karttunen, <a href="/A280694/b280694.txt">Table of n, a(n) for n = 1..15127</a>

%F a(n) = n / A280695(n).

%F Other identities. For all n >= 1:

%F a(A000032(n)) = A000032(n).

%F a(A057854(n)) = A280696(A057854(n)).

%F a(A000045(n)) = A280699(n).

%o (Scheme)

%o ;; A stand-alone program:

%o (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)))))

%Y Cf. A000032, A054494, A280695, A280699.

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

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 11 2017