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A105802 Smallest m such that the m-th Fibonacci number has exactly n divisors that are also Fibonacci numbers. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 8 20:00 EST 2023. Contains 360152 sequences. (Running on oeis4.)