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

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

1,2

Comments

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

Links

Table of n, a(n) for n=1..45.

Eric Weisstein's World of Mathematics, Fibonacci Number

Formula

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

Example

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.

Mathematica

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)

Crossrefs

Cf. A068499.

Sequence in context: A261955 A144615 A088698 * A285844 A285948 A285835

Adjacent sequences: A105799 A105800 A105801 * A105803 A105804 A105805

Keyword

nonn

Author

Reinhard Zumkeller, Apr 20 2005

Extensions

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

Status

approved