# Beat your Friend at Subtraction!

You and your friend are playing a game. The game goes as follows:

• At the start, you are given a positive integer $$N$$.
• You choose a positive factor $$n$$ of $$N$$, where $$n \neq N$$.
• You compute $$N - n$$ and give the result to your friend.
• Your friend repeats the above procedure with the integer she is given and gives the result to you, and so forth.

For example, if you are given $$N = 12,$$ you can choose $$n = 3$$ and give $$N - n = 9$$ to your friend. Then, $$N = 9$$.

Play continues in this fashion until one person is given $$N = 1$$, at which point that person loses.

Given that you and your friend will both play optimally, how many positive integers $$N \leq 2015$$ are there such that, when given at the start, you will always win?

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