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, 2025

Number theory Difficulty 5.0 AIME, harder Prove it United Kingdom

The sum of the factors of $2025$ is $1 + 3 + 5 + 9 + 15 + 25 + 27 + 45 + 75 + 81 + 135 + 225 + 405 + 675 + 2025 = 3751$ , which is an odd number. What is the smallest number $N > 2025$ for which the sum of the factors of $N$ is odd?

This is an Olympiad problem, so you must show that your value of $N$ has an odd sum of factors, and that no other value between 2025 and N does.

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