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Numbers k that divide phi(Fibonacci(k)).
2

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

%S 1,10,11,12,14,15,18,20,21,22,24,25,26,27,28,29,30,33,34,35,36,37,38,

%T 39,40,41,42,44,45,46,48,49,50,51,52,53,54,55,56,58,60,62,63,64,65,66,

%U 67,68,69,70,72,73,74,75,76,77,78,80,81,82,84,85,86,88,89,90,91,92,93

%N Numbers k that divide phi(Fibonacci(k)).

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

%H Amiram Eldar, <a href="/A075775/b075775.txt">Table of n, a(n) for n = 1..1343</a>

%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.

%t Select[Range[100],Divisible[EulerPhi[Fibonacci[#]],#]&] (* _Harvey P. Dale_, Jun 11 2015 *)

%Y Cf. A000010, A000045, A065449.

%K easy,nonn,changed

%O 1,2

%A _Benoit Cloitre_, Oct 09 2002