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\sigma_k(n)/ n^{k+2} (2020n + 2019)^2 > m 2020 MBMT p43

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February 13, 2022
number theoryMBMT

Problem Statement

Let σk(n)\sigma_k(n) be the sum of the kthk^{th} powers of the divisors of nn. For all k≥2k \ge 2 and all n≥3n \ge 3, we have that σk(n)nk+2(2020n+2019)2>m.\frac{\sigma_k(n)}{n^{k+2}} (2020n + 2019)^2 > m. Find the largest possible value of mm.
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