A074698 Numbers k that divide the number of divisors of Fibonacci(k).

1, 24, 48, 60, 64, 96, 128, 192, 256, 336, 384, 512, 576, 768, 1024, 1536, 1920, 2048, 3072

Offset: 1

Author

Benoit Cloitre, Sep 03 2002

Keywords

• nonn
• more

Comments

Are all numbers of the form 2^m*24 and 2^m*64, m >= 0, in the sequence?

This sequence is infinite (Luca, 2002). - Amiram Eldar, Jan 12 2022

Links

• Florian Luca, Problem H-590, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 40, No. 5 (2002), p. 472; Arithmetic Functions of Fibonacci Numbers, Solution to Problem H-590 by J.-Ch. Schlage-Puchta and J. Spilker, ibid., Vol. 41, No. 4 (2002), pp. 382-384.

Crossrefs

Cf. A000005, A000045, A063375.

Programs

Maple

with(combinat): with(numtheory): a:=proc(n) if type(tau(fibonacci(n))/n,integer) then n fi end: seq(a(n),n=1..200); # Emeric Deutsch, Jan 30 2006

Mathematica

With[{nn=200},Select[Thread[{DivisorSigma[0,Fibonacci[Range[nn]]],Range[nn]}],Divisible[#[[1]],#[[2]]]&]][[All,2]] (* The program generates the first 8 terms of the sequence. To generate more, increase the value of nn but the program may take a long time to run. *) (* Harvey P. Dale, Feb 17 2021 *)

PARI

isok(n) = ! (numdiv(fibonacci(n)) % n); \\ Michel Marcus, Sep 10 2017

Extensions

a(9) from Emeric Deutsch, Jan 30 2006

a(10)-a(19) from Charles R Greathouse IV, Nov 07 2016