9 has the three factors 1,3 and 9 is one. 25 (1,5,25) is another. 7*7 = 49, 11*11 = 121. In general, all squares of primes (other than 2).
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Yes. Square numbers have an odd number of factors. 49 has three factors.
A prime number has exactly two factors, 1 and the number itself.
The number of factors can be either even or odd.
21. Its factors are 1, 3, 7 and 21 which add to 32.
Start with the factors. Multiply combinations of three prime factors, then combinations of five, then seven, etc. All generated numbers will be guaranteed to have an odd number of prime factors.