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Ok

So I’m gonna share something cool as ice. I actually found this 2 years ago but never posted it.


Let me introduce this nice thing

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This sum is actually very nice. He wears a tie.

In fact if you input x=10^{-3}, and you would get this:

0.001002002003002004002004003004002006002004004005002006002006004004002008003004004006002008002006004004004009002004004008002008002006006004002010003006004006002008004008004004002012...

Ok so what’s dis? Notice that the decimals follow some pattern:

00, number, 00, number, 00, number….. And then we have some exceptions where “00” is replaced with “0” or “000”

What’s dis? There must be a pattern to the numbers right?

Let’s list down the number and see:

1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 8, 3, 4, 4, 6, 2, 8, 2, 6, 4, 4, 4, 9, 2, 4, 4, 8, 2, 8, 2, 6, 6, 4, 2, 10, 3, 6, 4, 6, 2, 8, 4, 8, 4, 4, 2, 12

There doesn’t seem to be a pattern is there?

BUT YOU’RE WRONG THERE IS A PATTERN

Let’s start with the first number:

  • 1: The number 1 has 1 divisor
  • 2: The number 2 has 2 divisor
  • 2: The number 3 has 3 divisor
  • 3: The number 4 has 3 divisor
  • 2: The number 5 has 2 divisor
  • 4: The number 6 has 4 divisor

Turns out that the nth number in the sequence is the number of divisors of n!

Cool right? Now why is dis so? Try to figure it out urselfgdby.