Given a positive interger N if it can be written as a sum of consecutive positive integers, then the maximum number could be:
1 + 2 + ...... + k = N
So the maximum K = ceil(0.5 * (-1 + sqrt(8*N))). Then the possible number would be from 1 to K.
Then for a given k within [1, K]:
m + m+1 + ...... + m+k-1 = N
m = (2*N - k**2 + k) / (2*k)
m must be an int. We just check m == int(m) for a given k