Derivation of certain sums "the hard way" – mathoverflow.net

It is a well-known fact, that one can derive some spectacular identities, e. g. $\sum^{n-1}_{m=1}\sigma_3(m)\sigma_3(n-m)=\frac {\sigma_7(n)-\sigma_3(n)}{120}$ $\sum^{n-1}_{m=1}\sigma_3(m)\...

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