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P14 [Number Theory] - Turkish NMO 1st Round - 2013

Source:

April 17, 2013
calculusintegrationfunction

Problem Statement

Let d(n)d(n) be the number of positive integers that divide the integer nn. For all positive integral divisors kk of 6480064800, what is the sum of numbers d(k)d(k)?
<spanclass=′latex−bold′>(A)</span> 1440<spanclass=′latex−bold′>(B)</span> 1650<spanclass=′latex−bold′>(C)</span> 1890<spanclass=′latex−bold′>(D)</span> 2010<spanclass=′latex−bold′>(E)</span> None of above <span class='latex-bold'>(A)</span>\ 1440 \qquad<span class='latex-bold'>(B)</span>\ 1650 \qquad<span class='latex-bold'>(C)</span>\ 1890 \qquad<span class='latex-bold'>(D)</span>\ 2010 \qquad<span class='latex-bold'>(E)</span>\ \text{None of above}
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