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Mock AIME 1 2005-2006/Problem 7

Revision as of 22:37, 17 April 2009 by Aimesolver (talk | contribs) (New page: == Problem == Let <math>f(n)</math> denote the number of divisors of a positive integer n. Evaluate f(f(<math>2006^{6002}</math>)). == Solution == <math>2006</math> = <math>2*17*59</m...)
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Problem

Let $f(n)$ denote the number of divisors of a positive integer n. Evaluate f(f($2006^{6002}$)).


Solution

$2006$ = $2*17*59$, so $f(2006^6002)$ has $6003^3$ positive divisors. $6003$ = $(3^2)(667)$ so $6003^3$ has $(6+1)(1+1)$, or $\boxed {021}$ divisors.

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