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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