F(1) = F(6) = F(3) = F(8) = F(4) = F(2) = F(1).
arrange in ascending order
1,2,3,4,6,8
Take n=5
5,10,5,10,5,10
Take n=5
7,12,6,3 F(6) matches in both so same both belongs to same value.
Take n=9
9,14,7 F(7) matches in both so same both belongs to same value.
We can see we have different value for multiples of 5 and other natural numbers.