Square numbers
16, 25, 36, 49, 64, 81, 100
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There are 19 numbers between zero and 365 that have an odd number of factors.
Perfect squares have odd numbers of factors. The perfect squares less than 100 are: 1,4,9,16,25,36,49,64,81,100. 64 seems to fit both criteria.
There are 50.
97
The most factors any odd number less than 100 has is 6. There are 4 numbers which have 6 factors:45, 63, 75 & 99.