1. Write down the natural numbers from 360 to 630 that have an odd number of divisors.
$1.361,400,441,484,529,576$ and 625
1.【Solution】If $\mathrm{a}$ is a divisor of the natural number $\mathrm{n}$, then $\frac{n}{a}$ is also a divisor of $\mathrm{n}$. Therefore, the divisors $\mathrm{a}$ and $\frac{n}{a}$ can be paired. Only when $\mathrm{n}=\mathrm{a}^{2}$, $\mathrm{a}$ and $\frac{n}{\mathrm{a}}$ are equal. So, when $\mathrm{n}$ is not a perfect square, its divisors can be paired, making the number of divisors even; when $\mathrm{n}$ is a perfect square $\mathrm{a}^{2}$, its divisor $\mathrm{a}$ can only pair with itself, making the number of divisors odd. Between 360 and 630, there are 7 perfect squares $\left(19^{2}=361>360, 25^{2}=625<630, 25-19+1=7\right)$, so there are 7 numbers with an odd number of divisors, which are: $361,400,441,484,529,576$ and 625.