[seqfan] divisor convolution

John Conway conway at math.Princeton.EDU
Fri Sep 18 18:19:29 CEST 1998

On Fri, 18 Sep 1998, Christian G.Bower wrote:

> After working out formulas to the necklace sequences, I noticed it
> was common for the formulas to contain something like:
> sum{d|n}(a(n/d)*b(d))
> It occurred to me that this might be a good operation to define on
> sequences. Thus I'm defining "divisor convolution" or DCONV as follows:

   You're by no means the first to do this.  The operation is well-known,
and corresponds to multiplication of the corresponding Dirichlet series.
It takes multiplicative functions to other multiplicative functions.

   Oh - I think I see that you realised this (I presume your "generating
function" is the Dirichlet series).

     John  Conway

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