A074698 - OEIS

%I #36 Jan 05 2025 19:51:37

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

%T 3072

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

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

%C This sequence is infinite (Luca, 2002). - _Amiram Eldar_, Jan 12 2022

%H Florian Luca, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/40-5/advanced40-5.pdf">Problem H-590</a>, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 40, No. 5 (2002), p. 472; <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/41-4/advanced41-4.pdf">Arithmetic Functions of Fibonacci Numbers</a>, Solution to Problem H-590 by J.-Ch. Schlage-Puchta and J. Spilker, ibid., Vol. 41, No. 4 (2002), pp. 382-384.

%p 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

%t 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 *)

%o (PARI) isok(n) = ! (numdiv(fibonacci(n)) % n); \\ _Michel Marcus_, Sep 10 2017

%Y Cf. A000005, A000045, A063375.

%K nonn,more

%O 1,2

%A _Benoit Cloitre_, Sep 03 2002

%E a(9) from _Emeric Deutsch_, Jan 30 2006

%E a(10)-a(19) from _Charles R Greathouse IV_, Nov 07 2016