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The sum is 121.
The two consecutive numbers whose factors have the same sum are 8 and 9. The factors of 8 are 1, 2, 4, and 8, and their sum is 15. The factors of 9 are 1, 3, and 9, and their sum is also 15. Therefore, 8 and 9 are the consecutive numbers whose factors have the same sum.
never less than n
28 and 6 are factors of 336.
31