Yes Sir, There is One 1,000,000,000,000,000,000,000,001
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If by 'perfect number' you mean 'perfect SQUARE', then yes. 49 is an odd number and a perfect square.
It is not yet known:Whether there is an infinite number of even perfect numbersWhether there is any odd perfect number
It is unknown whether an odd perfect number actually exists. If an odd perfect number exists it will be extremely large, that is in excess of 10300.
No. Because 7 is not even a perfect number; it is conjectured (not proven) that there are no odd perfect numbers only even ones and 7 is an odd number - it has been proven that if there is an odd perfect number it has to be extremely large, much-much-much larger than 7)
81 is; Natural number, Perfect-square number, Perfect 4th root number, Perfect totient number, Odd Number, Composite Number, etc.