Difference between revisions of "Mock AIME 1 2005-2006/Problem 7"
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...) |
Aimesolver (talk | contribs) (→Solution) |
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== 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)(1+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)(1+1)</math>, or <math>\boxed {021}</math> divisors. |
Revision as of 22:37, 17 April 2009
Problem
Let 
denote the number of divisors of a positive integer n. Evaluate f(f(
)).
Solution
= 
, so 
has 
positive divisors. 
= 
so has 
, or 
divisors.
