28496 60 Stars Astrology Season Essay Winter Holidays Special "What Are Perfect Numbers?" Part 1

60stars  Astrology Season  Essay

English  version

By TOKYO-TANUKI

28496　60 Stars Astrology　Season Essay　Winter Holidays Special　"What Are Perfect Numbers?" Part 1

1.  I'm in the middle of this Season Essay, but I'll take one more break here.

I did give a bit of a heads-up on X (Twitter) earlier, you know.
Well, I'll start now.

You know about "Perfect Numbers", right?

6, 28, 496, 8128, .....

According to Wikipedia,
“It is a natural number whose sum of positive divisors (excluding itself) equals itself.”

That's what it says!

...Well, take "6" for example.

The divisors of 6 are 1, 2, 3, so
1 + 2 + 3 = 6

...That's basically how it works.

But why limit it to natural numbers? 

......That's unclear.

It's just always been that way... Well, I guess that's true.

Why is that?




2. For natural numbers, perfect numbers other than "6" can be expressed as the sum of consecutive positive odd cubes starting from 1.

Let's express it as an equation:

2⁸ = 1³ + 3³, 
496 = 1³ + 3³ + 5³ + 7³ 
8128 = 1³ + 3³ + 5³ + 7³ + 9³ + 11³ + 13³ + 15³........

Well, this is also written on Wikipedia.

But you know, it doesn't say why only "6" is different.

So, why is that?





3. What makes 6 different from the others is:
1+2+3 = 1×2×3........1+a+b = １×a×ｂ ??　

This resembles the story about the diagonals of a heptagon,
but that one is a+b = a·b, so maybe it's different.





4. So........ Tanu-chan arbitrarily assumes that the divisors of a perfect number don't need to be integers

6 = √3² + √2² + √1²

Let's push our delusion a bit further

6 = (√5)² + 1²

!?.....“Hmm?”

Maybe this needs more research?

Could "6" be some kind of turning point?

(To be continued.)

Tanu-chan💓 TOKYO-TANUKI💛