MathDB
Integer Divisor Function

Source: 2023 AMC 12A #22

November 9, 2023
AMCAMC 12AMC 12A2023 AMC2023 AMC 12Afunctions

Problem Statement

Let ff be the unique function defined on the positive integers such that ∑d∣nd⋅f(nd)=1\sum_{d\mid n}d\cdot f\left(\frac{n}{d}\right)=1 for all positive integers nn, where the sum is taken over all positive divisors of nn. What is f(2023)f(2023)?
<spanclass=′latex−bold′>(A)</span> −1536<spanclass=′latex−bold′>(B)</span> 96<spanclass=′latex−bold′>(C)</span> 108<spanclass=′latex−bold′>(D)</span> 116<spanclass=′latex−bold′>(E)</span> 144<span class='latex-bold'>(A)</span>~-1536\qquad<span class='latex-bold'>(B)</span>~96\qquad<span class='latex-bold'>(C)</span>~108\qquad<span class='latex-bold'>(D)</span>~116\qquad<span class='latex-bold'>(E)</span>~144
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