From taking breaks from preparing for a talk I have in geometry, I started toying a little bit with perfect numbers. We all know that 3^3+4^3+5^3=216=6^3 This and the well known pythogrean triplet 3^2+4^2=5^2. So I thought of toying a little bit with powers of three and two, and I found by coincidence that: 3^3+5^3+7^3=495= 496 -1 , where we all know that 496 is a perfect number. Then I thought ridicuosly that this can happen also for other perfect numbers, but to no a veil, for 6 we can't have powers of three which are distinct from each other, but we do have powers of 2, 6-1=2^2+1^2. So I thought to myself, maybe every perfect number minus 1 can be represented as powers of 3 or 2 of distinct natural numbers. For 28 we have 28-1=3^3=27. For 8128 we have 8128-1=19^3+8^3+7^3+6^3+5^3+4^3+2^3. All the above is sheer luck and coincidence, but this raises the conjecture: Every (even) perfect number minus one can be represented as a sum of distinct powers of 2 or 3 I don't have enough time to check for the next perfect number. I did the last calculation via google, check me that I don't have mistakes. Is this already known?