A076984 -id:A076984 - 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)

A076985 Smallest Fibonacci numbers having exactly n Fibonacci divisors.

Original entry on oeis.org

1, 2, 8, 610, 144, 1134903170, 46368, 14930352, 4807526976, 1952132532477489958194625524584538730388053593825001030592563956919572392152809678530, 1548008755920, 303124944601307480151388995590175408058857436768033423077509087810

Offset: 1

Amarnath Murthy, Oct 25 2002

nonn

a(n) = A000045(A105802(n)). - Reinhard Zumkeller, Apr 20 2005

			a(5) = 144 and the Fibonacci divisors are 1, 2, 3, 8 and 144.

Eric Weisstein's World of Mathematics, Fibonacci Number

Cf. A076984.

More terms from Sascha Kurz, Jan 26 2003
a(12) from Reinhard Zumkeller, Apr 20 2005
Typo in data corrected by Sean A. Irvine, Apr 24 2025

A105802 Smallest m such that the m-th Fibonacci number has exactly n divisors that are also Fibonacci numbers.

Original entry on oeis.org

1, 3, 6, 15, 12, 45, 24, 36, 48, 405, 60, 315, 192, 144, 120, 945, 180, 1575, 240, 576, 3072, 295245, 360, 1296, 12288, 900, 960, 25515, 720, 14175, 840, 9216, 196608, 5184, 1260, 17325, 786432, 36864, 1680, 31185, 2880, 127575, 15360, 3600, 99225

Offset: 1

Reinhard Zumkeller, Apr 20 2005

nonn

A076985(n) = A000045(a(n)); A076984(a(n)) = n.

			n=6: a(6) = 45, A076985(6) = A000045(45) = 1134903170,
A076984(45) = #{1,2,5,34,109441,1134903170} = #{fib(1),fib(2),fib(5),fib(9),fib(21),fib(45)} = 6.

Eric Weisstein's World of Mathematics, Fibonacci Number

Cf. A068499.

t=Table[s=DivisorSigma[0, n]; If[OddQ[n], s, s-1], {n, 1000000}]; lst={}; n=1; While[pos=Flatten[Position[t, n, 1, 1]]; Length[pos]>0, AppendTo[lst, pos[[1]]]; n++ ]; lst (Noe)

Conjecture: a(2k+1) = 3*2^(Prime[k-1]-1) for k>3. It appears that a(2k+1) = 3*2^k for k = {1,2,3,4,6,10,12,16,18,...} = A068499[n] Numbers n such that n! reduced modulo (n+1) is not zero. - Alexander Adamchuk, Sep 15 2006

More terms from T. D. Noe, Jan 18 2006

A356122 Number of Lucas divisors of the n-th Lucas number.

Original entry on oeis.org

2, 1, 2, 3, 2, 2, 4, 2, 2, 4, 3, 2, 4, 2, 3, 5, 2, 2, 5, 2, 3, 5, 3, 2, 4, 3, 3, 5, 3, 2, 6, 2, 2, 5, 3, 4, 5, 2, 3, 5, 3, 2, 6, 2, 3, 7, 3, 2, 4, 3, 4, 5, 3, 2, 6, 4, 3, 5, 3, 2, 6, 2, 3, 7, 2, 4, 6, 2, 3, 5, 5, 2, 5, 2, 3, 7, 3, 4, 6, 2, 3, 6, 3, 2, 6, 4, 3, 5, 3, 2, 8, 4, 3, 5, 3, 4, 4, 2, 4, 7

Offset: 0

Michel Marcus, Jul 27 2022

nonn

Daniel Suteu, Table of n, a(n) for n = 0..10000

Cf. A000032, A102460, A304092, A356062, A356123.

Cf. A076984 (similar for Fibonacci numbers).

L(n)=fibonacci(n+1)+fibonacci(n-1); \\ A000032
isld(n) = { my(u1=1, u2=3, old_u1); if(n<=2, sign(n), while(n>u2, old_u1=u1; u1=u2; u2=old_u1+u2); (u2==n)); }; \\ A102460
nbld(n) = sumdiv(n, d, isld(d)); \\ A304092
a(n) = nbld(L(n));

a(n) = if(n==1, return(1)); my(k=fibonacci(n+1)+fibonacci(n-1),c=0,x=2,y=1); while(x <= k, if(k%x == 0, c++); [x,y]=[y,x+y]); c; \\ Daniel Suteu, Aug 25 2022

a(n) = A304092(A000032(n)).

A062558 Number of nonisomorphic cyclic subgroups of dihedral group with 2n elements.

Original entry on oeis.org

2, 2, 3, 3, 3, 4, 3, 4, 4, 4, 3, 6, 3, 4, 5, 5, 3, 6, 3, 6, 5, 4, 3, 8, 4, 4, 5, 6, 3, 8, 3, 6, 5, 4, 5, 9, 3, 4, 5, 8, 3, 8, 3, 6, 7, 4, 3, 10, 4, 6, 5, 6, 3, 8, 5, 8, 5, 4, 3, 12, 3, 4, 7, 7, 5, 8, 3, 6, 5, 8, 3, 12, 3, 4, 7, 6, 5, 8, 3, 10, 6, 4, 3, 12, 5, 4, 5, 8, 3, 12, 5, 6, 5, 4, 5, 12, 3, 6, 7, 9, 3

Offset: 1

Vladeta Jovovic, Jul 03 2001

nonn

Antti Karttunen, Table of n, a(n) for n = 1..1001

Cf. A000005, A000045, A023645, A062249 (labeled case).

One more than A076984.

a(n) = numdiv(n) + (n % 2) \\ Michel Marcus, Jun 17 2013

a(n) = A000005(n) + A000035(n) = tau(n)+(n mod 2), where tau(n) = the number of divisors of 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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A076985 Smallest Fibonacci numbers having exactly n Fibonacci divisors.

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A105802 Smallest m such that the m-th Fibonacci number has exactly n divisors that are also Fibonacci numbers.

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A356122 Number of Lucas divisors of the n-th Lucas number.

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A062558 Number of nonisomorphic cyclic subgroups of dihedral group with 2n elements.

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