A061899 Fibonacci numbers that are not squarefree.

8, 144, 2584, 46368, 75025, 832040, 14930352, 267914296, 4807526976, 12586269025, 86267571272, 225851433717, 1548008755920, 27777890035288, 498454011879264, 2111485077978050, 8944394323791464, 160500643816367088, 2880067194370816120, 4660046610375530309, 51680708854858323072

Offset: 1

Author

Asher Auel, May 20 2001

Keywords

• nonn

Comments

a(n) <= Fibonacci(6n) since 4 | Fibonacci(6n). Using other residue classes it can be shown that a(n) << 1.134^n. How far can this method be taken? - Charles R Greathouse IV, Dec 13 2011

Examples

			144 and 2584 are Fibonacci numbers (A000045) and are not squarefree: 144 = 2^4*3^2, 2584 = 2^3*17*19.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..328 (terms 1..87 from Harry J. Smith)

Crossrefs

Cf. A000045, A061305.

Programs

Mathematica

Select[Fibonacci[Range[100]],!SquareFreeQ[#]&] (* Harvey P. Dale, May 01 2018 *)

PARI

{ n=0; h=g=1; for (i=0, 375, f=g + h; h=g; g=f; if (!issquarefree(f), write("b061899.txt", n++, " ", f)) ) } \\ Harry J. Smith, Jul 28 2009

Formula

a(n) = A000045(A037917(n)). - R. J. Mathar, Jan 13 2014