# Consecutive Positive Integers

How many numbers from 1 to 1000 inclusive can be expressed as the sum of $$k \geq 2$$ consecutive positive integers for some value of $$k$$?

Details and assumptions

The value of $$k$$ can be different for each positive integer. E.g. $$3 = 1+2$$ and $$9 = 2+3+4$$ are both valid solutions.

The consecutive positive integers do not have to start from 1 (or 2).

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