[seqfan] Re: A106464

[Neil Sloane]

The formula  a(n)=sum{k=0..floor(n/2), gcd(n-k+1, k+1)}
suggests that this is the diag sums of a triangle
whose (n,k)th entry is something like gcd(n-k+1, k+1)  !

But why don't we ask Paul Barry directly?  He is still an active
contributor.  I will copy this to him.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Thu, May 10, 2018 at 6:42 PM, <israel at math.ubc.ca> wrote:

> Can somebody make sense out of A106464?
>
> A106464                 Diagonal sums of number triangle A029578.
> (but A029578 is not a triangle!)
>
> Data are
>         1, 1, 2, 3, 3, 4, 6, 6, 5, 11, 6, 9, 15, 12, 8, 18, 9, 21, 22, 15,
> 11, 32, 20, 18, 27, 31, 14, 45, 15, 32, 36, 24, 41, 57, 18, 27, 43, 60, 20,
> 66, 21, 51, 72, 33, 23, 84, 42, 60, 57, 61, 26, 81, 67, 88, 64, 42, 29,
> 135, 30, 45, 105
>
> with offset 0.  There is a formula given:
>
> a(n)=sum{k=0..floor(n/2), gcd(n-k+1, k+1)}
>
> but that doesn't match the Data: it would produce
> 1, 1, 3, 2, 6, 3, 8, 6, 11, 5, 17, 6, 16, 15, 20, 8, 27, 9, 31, 22, 26,
> 11, 44, 20, 31, 27, 45, 14, 60, 15, 48, 36, 41, 41, 75, 18, 46, 43, 80, 20,
> 87, 21, 73, 72, 56, 23, 108, 42, 85, 57, 87, 26, 108, 67, 116, 64, 71, 29,
> 165, 30, 76
>
> which is A060992 (without the first term 0).
>
> Cheers,
> Robert
>
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