A280696 -id:A280696 - cp's OEIS frontend

A280697 a(n) = n / A280696(n); n divided by its largest Lucas proper divisor, a(1) = 1.

1, 2, 3, 2, 5, 2, 7, 2, 3, 5, 11, 3, 13, 2, 5, 4, 17, 6, 19, 5, 3, 2, 23, 6, 25, 13, 9, 4, 29, 10, 31, 8, 3, 17, 5, 2, 37, 19, 13, 10, 41, 6, 43, 4, 15, 23, 47, 12, 7, 25, 17, 13, 53, 3, 5, 8, 19, 2, 59, 15, 61, 31, 9, 16, 65, 6, 67, 17, 23, 10, 71, 4, 73, 37, 25, 19, 7, 26, 79, 20, 27, 41, 83, 12, 85, 43, 3, 8, 89, 5, 13, 23, 31, 2, 95, 24, 97, 14, 9, 25, 101

Offset: 1

Antti Karttunen, Jan 11 2017

nonn

For n > 1, a(n) = n divided by the 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, A280695, A280696, A280687.

Scheme
```
(define (A280697 n) (/ n (A280696 n)))
```

a(n) = n / A280696(n).

A280686 Largest Fibonacci proper divisor of n, a(1) = 1.

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 1, 2, 3, 5, 1, 3, 1, 2, 5, 8, 1, 3, 1, 5, 3, 2, 1, 8, 5, 13, 3, 2, 1, 5, 1, 8, 3, 2, 5, 3, 1, 2, 13, 8, 1, 21, 1, 2, 5, 2, 1, 8, 1, 5, 3, 13, 1, 3, 5, 8, 3, 2, 1, 5, 1, 2, 21, 8, 13, 3, 1, 34, 3, 5, 1, 8, 1, 2, 5, 2, 1, 13, 1, 8, 3, 2, 1, 21, 5, 2, 3, 8, 1, 5, 13, 2, 3, 2, 5, 8, 1, 2, 3, 5, 1, 34, 1, 13, 21, 2, 1, 3, 1, 55, 3, 8, 1, 3, 5, 2

Offset: 1

Antti Karttunen, Jan 11 2017

nonn

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

			For n=3, the greatest Fibonacci number that divides 3 and is less than 3 is A000045(1)=A000045(2)=1, thus a(3) = 1.
For n=20, the greatest Fibonacci number that divides 20 and is less than 20 is A000045(5)=5, thus a(20) = 5.
For n=21, the greatest Fibonacci number that divides 21 and is less than 21 is A000045(4)=3, thus a(21) = 3.

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

Cf. A000045, A032742, A105800, A280687, A280696.

Cf. A001690 (gives the positions n > 1 where this sequence and A054494 obtain equal values).

a(n)=my(r=1,lim=if(n%2,n\3,n/2),a=1,b=2); while(bCharles R Greathouse IV, Jun 20 2017

;; A stand-alone program:
(define (A280686 n) (let loop ((f1 1) (f2 1) (lpd 1)) (cond ((>= f2 n) lpd) ((zero? (modulo n f2)) (loop f2 (+ f1 f2) f2)) (else (loop f2 (+ f1 f2) lpd)))))

a(n) = n / A280687(n).
Other identities. For all n >= 1:
a(A000045(n)) = A105800(n).
a(A001690(n)) = A054494(A001690(n)).

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).

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

A280697 a(n) = n / A280696(n); n divided by its largest Lucas proper divisor, a(1) = 1.

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A280686 Largest Fibonacci proper divisor of n, a(1) = 1.

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A280694 Largest Lucas number (A000032) dividing n.

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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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