35522

It seems that in this problem, all numbers except multiples of 8 (unless they are in another times table as well) can be written as a sum of consecutive numbers.
All odd numbers can be written as two consecutive numbers, because if two numbers are consecutive, 1 must be odd and 1 must be even, and odd + even always equals odd. This could be just one way of writing the nnumber, though.
There are lots of other patterns as well - this puzzle is a lot less random than it first appears.
For example, here are numbers with a difference of 4 (starting at 10). They all have 4 consecutive numbers which add together to make them.
10 - 1+2+3+4
14 - 2+3+4+5
18 - 3+4+5+6
22 - 4+5+6+7
In all the columns, each place adds 1 each time, so in total you add 4 each time. This pattern also works for numbers with a difference of 5, starting at 15, (5 consecutive numbers) and 6, starting at 21. This may go on for all numbers though!