201 numbers are less than 2017
If and only if it is odd, a number is the sum of two successive integers.
Only if it is a multiple of 5 is a number considered to be the sum of 5 consecutive integers. If you have any doubts, remember that the product of five consecutive integers equals five times the integer in the middle (this remains true if instead of 5 you put in any odd positive integer).
Consequently, you are seeking odd multiples of 5 below 2017. There are 403 multiples of 5 immediately below 2017, or 2015/5. Of those, 202 are odd. It is necessary to eliminate the number 5 because it is not completely positive when expressed as the sum of its successive integers, which is (-1)+0+1+2+3.
There are 201 numbers left.
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