Monday, April 04, 2016
Are perfect numbers bigger than 6 initial sums of odd cubes?
I pose two questions today (Monday April 4).
I will post the answers tomorrow (Tuesday April 5).
Feel free to comment about the answers. If you don't want clues look at the comments.
If I need to clarify something I will do it in the main post So, to reiterate- feel free to leave spoilers but if you want to avoid reading them, don't read the comments.
The first four perfect numbers are 6, 28, 496, 8128
28 = 13 + 33
496 = 13 + 33 + 53 + 73
Is 8128 the sum of the first six odd cubes? No, and that is not one of my questions.
1) Is there a k such that 8128 is the sum of the first k odd cubes?
2) Is there something interesting going on here?