Difference between revisions of "2021 Fall AMC 10A Problems/Problem 23"
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For each positive integer <math>n</math>, let <math>f_1(n)</math> be twice the number of positive integer divisors of <math>n</math>, and for <math>j \ge 2</math>, let <math>f_j(n) = f_1(f_{j-1}(n))</math>. For how many values of <math>n \le 50</math> is <math>f_{50}(n) = 12?</math> | For each positive integer <math>n</math>, let <math>f_1(n)</math> be twice the number of positive integer divisors of <math>n</math>, and for <math>j \ge 2</math>, let <math>f_j(n) = f_1(f_{j-1}(n))</math>. For how many values of <math>n \le 50</math> is <math>f_{50}(n) = 12?</math> | ||
<math>\textbf{(A) }7\qquad\textbf{(B) }8\qquad\textbf{(C) }9\qquad\textbf{(D) }10\qquad\textbf{(E) }11</math> | <math>\textbf{(A) }7\qquad\textbf{(B) }8\qquad\textbf{(C) }9\qquad\textbf{(D) }10\qquad\textbf{(E) }11</math> | ||
Revision as of 22:27, 22 November 2021
Problem
For each positive integer 
, let 
be twice the number of positive integer divisors of , and for 
, let 
. For how many values of 
is 
