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

1,1

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

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000045, A061305.

Sequence in context: A263604 A212703 A065409 * A134492 A067421 A124059

Adjacent sequences: A061896 A061897 A061898 * A061900 A061901 A061902

Keyword

nonn

Author

Asher Auel, May 20 2001

Status

approved