Difference between revisions of "Mock AIME 1 2005-2006/Problem 7"
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| − | <math>2006</math> = <math>2*17*59</math>, so <math>f(2006^{6002})</math> has <math>6003^3</math> positive divisors. <math>6003^3</math> = <math>(3^6)(23^3)(29^3)</math> so <math>6003^3</math> has <math>(6+1)(3+1)(3+1)</math>, or <math>\boxed {112}</math> divisors | + | <math>2006</math> = <math>2*17*59</math>, so <math>f(2006^{6002})</math> has <math>6003^3</math> positive divisors. <math>6003^3</math> = <math>(3^6)(23^3)(29^3)</math> so <math>6003^3</math> has <math>(6+1)(3+1)(3+1)</math>, or <math>\boxed {112}</math> divisors |
Revision as of 16:18, 9 February 2023
Problem
Let 
denote the number of divisors of a positive integer 
. Evaluate 
.
Solution
= 
, so 
has 
positive divisors. = 
so has 
, or 
divisors
