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Numbers n such that F(n) divides F(F(n)), where F(n) is a Fibonacci number.
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%I #13 Oct 09 2015 18:23:26

%S 1,2,5,12,24,25,36,48,60,72,96,108,120,125,144,168,180,192,216,240,

%T 288,300,324,336,360,384,432,480,504,540,552,576,600,612,625,648,660,

%U 672,684,720,768,840,864,900,960,972,1008,1080,1104,1152,1176,1200,1224,1296,1320

%N Numbers n such that F(n) divides F(F(n)), where F(n) is a Fibonacci number.

%C It is known that for n > 2 Fibonacci(n) divides Fibonacci(m) if and only if n divides m. Therefore if the term "2" is omitted this is identical to A023172, which see for further information. - _Stefan Steinerberger_, Dec 20 2007

%e 12 is a term because F(12) = 144 divides F(F(12)) = F(144) = 555565404224292694404015791808.

%p with(combinat): a:=proc(n) if type(fibonacci(fibonacci(n))/fibonacci(n), integer) then n else end if end proc: seq(a(n),n=1..40); # _Emeric Deutsch_, Aug 24 2007

%Y Cf. A023172. Cf. also A000045 = Fibonacci(n), A007570 = F(F(n)), where F is a Fibonacci number, A023172 = numbers n such that n divides Fibonacci(n).

%Y Cf. A263101.

%K nonn

%O 1,2

%A _Alexander Adamchuk_, May 13 2007

%E Edited by _N. J. A. Sloane_, Dec 22 2007