Slalom conjuncture

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The Slalom Conjecture was discovered during a math assignment. It states that if there is an odd square $n^2$, then this square has a maximum of $n^2 - 2n$ factors starting from 3.

Listed is a table of squares and factors up to 11.

Number $n^2$ # of factors
1 1 1
3 9 3
5 25 3
7 49 3
9 81 5
11 121 3
... ... ...
81 6561 9
4001 16008001 3

Notice that most of the squares, even 4001, have only 3 factors.

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