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%I #35 Jan 12 2022 08:53:41
%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://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://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