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

1,2

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

Table of n, a(n) for n=1..19.

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.

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 *)

Prog

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

Crossrefs

Cf. A000005, A000045, A063375.

Sequence in context: A105779 A199105 A329884 * A334759 A341296 A338853

Adjacent sequences: A074695 A074696 A074697 * A074699 A074700 A074701

Keyword

nonn,more

Author

Benoit Cloitre, Sep 03 2002

Extensions

a(9) from Emeric Deutsch, Jan 30 2006

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

Status

approved