A061899 - OEIS

%I #37 Oct 27 2023 22:00:46

%S 8,144,2584,46368,75025,832040,14930352,267914296,4807526976,

%T 12586269025,86267571272,225851433717,1548008755920,27777890035288,

%U 498454011879264,2111485077978050,8944394323791464,160500643816367088,2880067194370816120,4660046610375530309,51680708854858323072

%N Fibonacci numbers that are not squarefree.

%C 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

%H Amiram Eldar, <a href="/A061899/b061899.txt">Table of n, a(n) for n = 1..328</a> (terms 1..87 from Harry J. Smith)

%F a(n) = A000045(A037917(n)). - _R. J. Mathar_, Jan 13 2014

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

%t Select[Fibonacci[Range[100]],!SquareFreeQ[#]&] (* _Harvey P. Dale_, May 01 2018 *)

%o (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

%Y Cf. A000045, A061305.

%K nonn

%O 1,1

%A _Asher Auel_, May 20 2001