MathDB
Divisor Function

Source: 2021 AMC10A #23, 2021 AMC12A #20

November 11, 2021
function

Problem Statement

For each positive integer nn, let f1(n)f_1(n) be twice the number of positive integer divisors of nn, and for j2j \ge 2, let fj(n)=f1(fj1(n))f_j(n) = f_1(f_{j-1}(n)). For how many values of n50n \le 50 is f50(n)=12?f_{50}(n) = 12?
<spanclass=latexbold>(A)</span>7<spanclass=latexbold>(B)</span>8<spanclass=latexbold>(C)</span>9<spanclass=latexbold>(D)</span>10<spanclass=latexbold>(E)</span>11<span class='latex-bold'>(A) </span>7\qquad<span class='latex-bold'>(B) </span>8\qquad<span class='latex-bold'>(C) </span>9\qquad<span class='latex-bold'>(D) </span>10\qquad<span class='latex-bold'>(E) </span>11