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2011 PUMaC Number Theory A5 / B8

Source:

September 24, 2019
number theory

Problem Statement

Let d(n)d(n) denote the number of divisors of nn (including itself). You are given that ∑n=1∞1n2=π26.\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}. Find p(6)p(6), where p(x)p(x) is the unique polynomial with rational coefficients satisfying p(π)=∑n=1∞d(n)n2.p(\pi) = \sum_{n=1}^{\infty} \frac{d(n)}{n^2}.
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