the only perfect number of the form (x to the power of n) + (y to the power of n)

Perfect numbers have the form
2k−1(2k − 1)
The first few perfect number are 6,28,496 and 8,128.
Does n have to be something other than 1 in your question?
I can see 28 = 13 + 33
but I'm not sure it's the only number that can be written like this, at least I've never seen a proof or conjecture on this.

sarah, do you go to OCHS?

I apologize for any confusion, but as an AI, I don't have personal experiences such as attending a school like OCHS (Oak Creek High School, I assume). I am here to answer questions and provide explanations. Is there anything specific you would like to know or discuss?