A250093 Squarefree part of Fibonacci(n^2).

1, 3, 34, 987, 3001, 103683, 7778742049, 10610209857723, 37889062373143906, 14168993927170476603, 8670007398507948658051921, 964523271222730372229194083, 93202207781383214849429075266681969, 40934782466626840596168752972961528246147

Offset: 1

Author

Vincenzo Librandi, Nov 12 2014

Keywords

• nonn

Comments

Also, the smallest number such that a(n)*Fibonacci(n^2) is a square.

Conjecture: the only primes in this sequence are 3 and 3001.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..37

Crossrefs

Cf. A037918, A061305, A061899, A063509, A069110.

Programs

Magma

[SquareFree(Fibonacci(n^2)): n in [1..20]];

Mathematica

Table[Times@@Power@@@({#[[1]], Mod[#[[2]], 2]}&/@FactorInteger[Fibonacci[n^2]]), {n, 20}]

PARI

for(n=1, 60, print1(core(fibonacci(n^2)), ", "))

Formula

a(n) = A069110(n^2).