[seqfan] Re: Lists of sums

[David Seal]

I can offer a succinct definition of your second sequence: a(1) = 1, a(n) is the sum of m such that 2 <= m <= n and GPF(m) = GPF(n), where GPF(i) is the greatest prime factor of i (A006530).

Best regards,

David


> On 21 October 2019 at 20:24 jnthn stdhr <jstdhr at gmail.com> wrote:
> 
> 
> Hi folks.
> 
> I will add either, or both, of these, if of interest.  Name suggestions
> would be helpful, in that case.
> 
> a(n) = 1, 3, 6, 4, 11, 10, 18, 8, 17, 20, 29, 12, 42, 34, 32, 28, 59,...
> 
> Superseeker yields a blank stare.
> 
> Here's what I did:
> 
> If n = 0, 1, or a prime, start a column.  For each composite, find the
> largest prime factor p and place n in column "p."
> a(n) is then the sum m of all numbers in the same row as m.
> 
> At n=20 it looks like this:
> 
>                   18
>            16   12  20
>             8    9    15
>             4    6    10   14
> 0    1    2    3    5     7    11   13  17  19
> 
> Summing columns as we go gives:
> 
> a(n) = 0, 1, 2, 3, 6, 5, 9, 7, 14, 18, 15, 11, 30, 13, 21, 30, 17,...
> 
> Also not in the database.
> 
> -Jonathan
> 
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