. Find all numbers from 1 to 100 that have an odd number of positive divisors.
. If $a$ is a divisor of $N$, then $N / a$ is also a divisor. Thus, the divisors are distributed in pairs. The only exception is when $a=N / a$, in other words, $N=a^{2}$. In this case, $a$ is the only divisor that does not have a pair. Therefore, $N$ has an odd number of positive divisors if and only if it is a perfect square. The numbers that answer the question are thus $1,4,9,16,25,36,49$, 64,81 and 100.