Dirichlet It Everytime

\[ \displaystyle \sum_{n=1}^\infty \dfrac{\sigma_{2016} (n)}{n^{M}} \]

Let \(\sigma_A(n) \) denote the sum of \(A^\text{th} \) powers of all the positive integer divisors of \(n\). For example, \(\sigma_5(6) = 1^5 + 2^5 + 3^5 + 6^5 = 8052\). Find the infimum of \(M\) such that the series above converges.


Inspiration.

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