A127787 Numbers n such that F(n) divides F(F(n)), where F(n) is a Fibonacci number.

1, 2, 5, 12, 24, 25, 36, 48, 60, 72, 96, 108, 120, 125, 144, 168, 180, 192, 216, 240, 288, 300, 324, 336, 360, 384, 432, 480, 504, 540, 552, 576, 600, 612, 625, 648, 660, 672, 684, 720, 768, 840, 864, 900, 960, 972, 1008, 1080, 1104, 1152, 1176, 1200, 1224, 1296, 1320

Offset: 1

Author

Alexander Adamchuk, May 13 2007

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

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).

Cf. A263101.

Programs

Maple

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

Extensions

Edited by N. J. A. Sloane, Dec 22 2007