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 17:18, 9 February 2023
Problem
Let denote the number of divisors of a positive integer
. Evaluate
.
Solution
=
, so
has
positive divisors.
=
so
has
, or
divisors