Difference between revisions of "Mock AIME 1 2005-2006/Problem 7"
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== Problem == | == Problem == | ||
| − | Let <math>f(n)</math> denote the number of divisors of a positive integer <math>n</math>. Evaluate <math>f(f(2006^{6002}</math> | + | Let <math>f(n)</math> denote the number of divisors of a positive integer <math>n</math>. Evaluate <math>f(f(2006^{6002}))</math>. |
== Solution == | == Solution == | ||
<math>2006</math> = <math>2*17*59</math>, so <math>f(2006^{6002})</math> has <math>6003^3</math> positive divisors. <math>6003</math> = <math>(3^2)(667)</math> so <math>6003^3</math> has <math>(6+1)(2+1)</math>, or <math>\boxed {021}</math> divisors. | <math>2006</math> = <math>2*17*59</math>, so <math>f(2006^{6002})</math> has <math>6003^3</math> positive divisors. <math>6003</math> = <math>(3^2)(667)</math> so <math>6003^3</math> has <math>(6+1)(2+1)</math>, or <math>\boxed {021}</math> divisors. | ||
Revision as of 22:39, 17 April 2009
Problem
Let 
denote the number of divisors of a positive integer 
. Evaluate 
.
Solution
= 
, so 
has 
positive divisors. 
= 
so has 
, or 
divisors.
