MathDB
P30 [Number Theory] - Turkish NMO 1st Round - 2014

Source:

May 26, 2014

Problem Statement

Let s(n)s(n) denote the number of positive divisors of positive integer nn. What is the largest prime divisor of the sum of numbers (s(k))3(s(k))^3 for all positive divisors kk of 201420142014^{2014}?
<spanclass=latexbold>(A)</span> 5<spanclass=latexbold>(B)</span> 7<spanclass=latexbold>(C)</span> 11<spanclass=latexbold>(D)</span> 13<spanclass=latexbold>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 5 \qquad<span class='latex-bold'>(B)</span>\ 7 \qquad<span class='latex-bold'>(C)</span>\ 11 \qquad<span class='latex-bold'>(D)</span>\ 13 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}