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Three consecutive positive integers are raised to the first, second and third powers respectively and then added. The sum so obtained is a perfect square root equals to the total of the three originals integers. Which of the following best describes the minimum, say m, of these three integers?

1. $1 \leq m \leq 3$
2. $4 \leq m \leq 6$
3. $7 \leq m \leq 9$
4. $10 \leq m \leq 12$
5. $13 \leq m \leq 15$

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