[seqfan] Re: sequence based on A050873 triangular array for GCD(u, v)

[Olivier Gerard]

I resend Jamie Morken's message at his suggestion
hoping it will appear this time will all the necessary
line feeds.

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Hi,

For the sequence A050873, I'd like to propose a sequence based on it,
but am not sure what the formula for the sequence is, and need help to
find some more terms.

Here is the sequence so far:

n a(n)
1 1
2 2
3 6
4 12
5 30
6 60
7 210
8 840
9 612
10 420
11 2310

For prime n, a(n) is a Primorial number.

Example of how to construct the sequence from A050873, for n = 3

Use the first 3 columns of A050873 starting at row 3 and identify the count
of consecutive rows until a repeating pattern occurs.

1 1 3
1 2 1
1 1 1
1 2 3
1 1 1
1 2 1

The first three columns of A050873 starting at the third row is a
repetition of those 6 rows, so the next row is 1 1 3.

Example for n = 11

Use the first 11 columns of A050873 starting at row 11:

1 1 1 1 1 1 1 1 1 1 11
1 2 3 4 1 6 1 4 3 2 1

1 1 1 1 1 1 1 1 1 1 1
1 2 1 2 1 2 7 2 1 2 1
...

It takes 2310+1 rows before the patterns shows up and then the first eleven
columns starting
at the eleventh row is a repetition of those 2310 rows.

The prime rows have a Pn row count for the repetition, but calculating the
non prime column
row counts like above seems harder, I don't know if there is a formula for
it like for the prime
columns row counts, but maybe someone can find it or could calculate more
values of the
sequence.  Thanks.

cheers,
Jamie

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