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A074698
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Numbers k that divide the number of divisors of Fibonacci(k).
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2
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1, 24, 48, 60, 64, 96, 128, 192, 256, 336, 384, 512, 576, 768, 1024, 1536, 1920, 2048, 3072
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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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.
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(PARI) isok(n) = ! (numdiv(fibonacci(n)) % n); \\ Michel Marcus, Sep 10 2017
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CROSSREFS
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Cf. A000005, A000045, A063375.
Sequence in context: A105779 A199105 A329884 * A334759 A341296 A338853
Adjacent sequences: A074695 A074696 A074697 * A074699 A074700 A074701
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KEYWORD
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nonn,more
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AUTHOR
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Benoit Cloitre, Sep 03 2002
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EXTENSIONS
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a(9) from Emeric Deutsch, Jan 30 2006
a(10)-a(19) from Charles R Greathouse IV, Nov 07 2016
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STATUS
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approved
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