A111077 Smallest squarefree integer > the n-th term of the Fibonacci sequence.

1, 2, 2, 3, 5, 6, 10, 14, 22, 35, 57, 91, 145, 235, 379, 611, 989, 1598, 2585, 4182, 6766, 10947, 17713, 28658, 46369, 75026, 121394, 196419, 317813, 514230, 832042, 1346270, 2178310, 3524579, 5702889, 9227467, 14930353, 24157819, 39088171

Offset

0,2

Links

Table of n, a(n) for n=0..38.

Example

a(4) = 5 because 5 is the smallest squarefree integer greater than 3, the 4th number of the Fibonacci sequence.

Maple

with(numtheory): with(combinat): a:=proc(n) local B, j: B:={}: for j from 1+fibonacci(n) to 20+fibonacci(n) do if abs(mobius(j))>0 then B:=B union {j} else B:=B fi od: B[1]: end: seq(a(n), n=0..43); # Emeric Deutsch, Oct 11 2005

Mathematica

f[n_] := Block[{k = Fibonacci[n] + 1}, While[ Union[Last /@ FactorInteger[k]][[ -1]] > 1, k++ ]; k]; Table[ f[n], {n, 0, 38}] (* Robert G. Wilson v *)
ssi[n_]:=Module[{k=n+1}, While[!SquareFreeQ[k], k++]; k]; ssi/@Fibonacci[ Range[0, 40]] (* Harvey P. Dale, Apr 12 2015 *)

Crossrefs

Cf. A000045, A005117.

Sequence in context: A241652 A241636 A227360 * A283189 A032157 A153926

Adjacent sequences: A111074 A111075 A111076 * A111078 A111079 A111080

Keyword

nonn

Author

Joseph Buszka (jab5118(AT)psu.edu), Oct 11 2005

Extensions

More terms from Robert G. Wilson v and Emeric Deutsch, Oct 11 2005

Status

approved