[seqfan] Re: A recurrence for the Dirichlet inverse of the Euler totient function.

[Mitch Harris]

Looking at the OEIS entries, I dont see the connection with the Mahonian numbers. Can you've more of how the recurrences are connected?

Mitch

On Jun 17, 2011, at 4:24 PM, "Mats Granvik" <mgranvik at abo.fi> wrote:

> This Mathematica program generates the Dirichlet inverse of the Euler 
> totient function as the main diagonal of a symmetric array with 
> periodic columns and rows: https://oeis.org/A023900. The recurrence is 
> related to the recurrence for the Mahonian numbers: 
> https://oeis.org/A008302
> 
> By changing signs in front of the sums we can get the
> Fredholm-Rueppel sequence. https://oeis.org/A036987
> 
> Mats Granvik
> 
> Mathematica program:
> 
> Clear[t, n, k, a, b];
> nn = 50;
> t[n_, 1] = 1;
> t[1, k_] = 1;
> t[n_, k_] :=
>    t[n, k] =
>     If[n < k,
>      If[And[n > 1, k > 1], Sum[-t[k - i, n], {i, 1, n - 1}], 0],
>      If[And[n > 1, k > 1], Sum[-t[n - i, k], {i, 1, k - 1}], 0]];
> a = Flatten[Table[Table[t[n, k], {k, n, n}], {n, 1, nn}]];
> a
> Sign[a]
> b = MoebiusMu[
>     Prepend[Array[Times @@ First[Transpose[FactorInteger[#]]] &,
>       nn - 1, 2], 1]];
> Sign[a] - b
> 
> 
> 
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