51. Just add two to an odd number to work out the next ;)
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The answer is 49.
Square numbers, like 49, have an odd number of factors.
Yes. Square numbers have an odd number of factors. 49 has three factors.
If by 'perfect number' you mean 'perfect SQUARE', then yes. 49 is an odd number and a perfect square.
Next odd number after 999 is 1001