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

1,2

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

Links

Table of n, a(n) for n=1..55.

Example

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

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

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.

Sequence in context: A357288 A326510 A112287 * A116733 A116721 A294868

Adjacent sequences: A127784 A127785 A127786 * A127788 A127789 A127790

Keyword

nonn

Author

Alexander Adamchuk, May 13 2007

Extensions

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

Status

approved