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Tagged with arithmetic-functions convolution
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Are there multiplicative functions which are not rational?
Vaidyanathaswamy calls an arithmetic function rational if it is the convolution of some finite collection of functions which are either completely multiplicative or inverse to a completely ...
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Is there a closed form for the discrete convolution of $\sigma_1$ and $\sigma_2$?
I am trying to find a closed form for the following sum:
$$\sum_{k = 1}^{n-1}\sigma_1(k) \sigma_2(n-k)$$
where $\sigma_i$ is the sum of divisors and $\sigma_2$ is the sum of squares of divisors.
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