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A particularly "natural" algebraic structure with three commutative,...
EDIT: As mentioned in my answer below, I was mistaken in thinking Dirichlet convolution distributes over ordinary convolution. I'm leaving this question here for reference.I keep stumbling on the same...
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Ack - Dirichlet convolution does NOT distribute over ordinary convolution. I went wrong somewhere way in the beginning of this process and need to backtrack.See below, where sequences are indexed...
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