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An arithmetic function is one whose domain is the positive integers and whose range is a subset of the complex numbers. There are a number of important number-theoretic examples.

11 votes
3 answers
700 views

Evaluating the sum of $kl^2$ over $p,q,k,l$ such that $pk +ql = n$

I have come across the following sum: $$\sum_{\substack{p, q, k, l \in \mathbb{N} \\ k > l \\ pk + ql = n}}kl^2$$ and I am trying to simplify it, hoping to get a nice formula in terms of $n$ and som …
metallicmural99's user avatar
3 votes
0 answers
231 views

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. Le …
metallicmural99's user avatar