So it occurred to me recently that 21 kinda stands out among among its nearby neighbors in that there are several sets of consecutive positive integers that can be summed to equal 21 -- namely 1+2+3+4+5+6, 6+7+8, and 10+11. So I started thinking - "I wonder if all numbers can be written as a summation of two or more consecutive integers." Thanks to a quick Matlab script I figured out that there are certain numbers that can not be represented as such. Actually they are a pretty obvious set of numbers. (I will not mention what the set is because anyone who is interested in answering my main question will figure this out anyway.) 


So I had fun proving that this "obvious" set could never be represented as a summation of consecutive numbers -- no small task for me although I'm sure it will be simple for some of you. However I could not prove that the numbers in the "obvious" set were the *only* ones that can not be represented as the sum of two or more consecutive integers. Can anyone show me how such a proof would be performed?



Summation of consecutive positive integers
The number of ways of writing *n* as a sum of [more than one] consecutive positive integers
is equal to the number of odd divisors of *n* [that are greater than one].


