# Did you count your hops?

Hoppy the Rabbit lives on the vertices of a regular 2015-gon with vertices labelled $$1,2,3,4\dots 2015$$. Hoppy lives on vertex 1, and he wishes to visit every vertex this year. To do this he buys a $$k$$-hopping machine. The $$k$$-hopping machine allows Hoppy to hop from his current vertex (assume it has number $$v$$) to the vertex with the number $$v+k$$. If $$v+k>2015$$ it sends him to vertex $$v+k-2015$$ instead. The $$k$$ hopping machines exist for $$k=1,2,3\dots 2015$$. What is the sum of the values of $$k$$ for which the $$k$$-hopping machine allows Hoppy to reach all of the vertices, starting at vertex 1 and hopping a finite number of times?

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