No.
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If you have a number like 12 and you multiply it by the same number: 12 and the answer you get is a whole number, then the whole number is the perfect square.
12 is not a perfect square.
12 is not a perfect square, so there is no such number
Any number can be squared, but 12 is not a perfect square(I.E 3X3=9,4X4=16)
If by 'perfect number' you mean 'perfect SQUARE', then yes. 49 is an odd number and a perfect square.