method for Möbius transform

[Davide Rotondo]

Hi to all! Here is a procedure to obtain the Moebius transform of primes. What do you think? Does it works?

I started with a diagonal of 2 where in the following rows I rewrite the numbers from the first row interspersed with one 0, two 0s, three 0s, and so on.

2
0 2
0 0 2
0 0 0 2
0 0 0 0 2
0 0 0 0 0 2
0 0 0 0 0 0 2
...

The sum of the numbers in the first column gives 2, which is the first prime number. Now I want to see which number, added to 2 in the second column, will give 3, which is the prime number after 2, and I get 1.

Therefore, I will have

2 1
0 2 0 1
0 0 2 0 0 1
0 0 0 2 0 0 0 1
0 0 0 0 2 0 0 0 0 1
...

It's a construction procedure.

a) 2

b) 2

    0 2

C) 2 1

     0 2

d) 2 1 3

    0 2 0

    0 0 2

e) 2 1 3 4

    0 2 0 1

    0 0 2 0

    0 0 0 2

...

See you soon

Davide

[Davide Rotondo]

Hi to all, any news about this conversation?

See you soon

Davide

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[Davide Rotondo]

Hi to all, any news about this conversation?

See you soon

Davide

[Geoffrey Caveney]

If one performs this Möbius transform method for squares, it produces the well-known sequence A007434, the Jordan function J_2(n).

Davide's method is already in OEIS as A007444, the Möbius transform of primes.

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[Davide Rotondo]

Dear Geoffrey, I wonder if the visual method I used is known? What do you think?

See you soon

Davide

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