Some numbers can be expressed as the sum of a string of consecutive positive numbers. Which numbers have this property?

Question

anonymous · Answer

For example:
$$9=2+3+4$$$$11=5+6$$$$18=3+4+5+6$$

akshay_budhkar · Answer

sum of how many consecutive numbers?

anonymous · Answer

Any amount. Try doing all the numbers from 1-20. I think you'll see something interesting.

akshay_budhkar · Answer

no no i am right..... all numbers except the power of 2!

anonymous · Answer

We have a winrar! There is some property of powers of 2 that makes them unable to be the sum of consecutive positive numbers. Bonus imaginary points if you can figure out what that property is

akshay_budhkar · Answer

lol.. i will try finding it.. wait

akshay_budhkar · Answer

give up dalvoron..:(

anonymous · Answer

Powers of two have no odd factors besides 1!

akshay_budhkar · Answer

lol
we all know that! but whats the connection here?

anonymous · Answer

That's it. Any number that has an odd factor that isn't 1 can be expressed as a sum of consecutive positive numbers. Simples!