MathDB
2013-2014 Fall OMO #19

Source:

October 30, 2013
Online Math OpenfunctionEulernumber theoryrelatively primegeometric series

Problem Statement

Let σ(n)\sigma(n) be the number of positive divisors of nn, and let rad⁡n\operatorname{rad} n be the product of the distinct prime divisors of nn. By convention, rad⁡1=1\operatorname{rad} 1 = 1. Find the greatest integer not exceeding 100(∑n=1∞σ(n)σ(nrad⁡n)n2σ(rad⁡n))13. 100\left(\sum_{n=1}^{\infty}\frac{\sigma(n)\sigma(n \operatorname{rad} n)}{n^2\sigma(\operatorname{rad} n)}\right)^{\frac{1}{3}}. Proposed by Michael Kural
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