MathDB

9

Part of 2019 AIME Problems

Problems(2)

Equation in tau

Source: 2019 AIME I #9

3/14/2019
Let τ(n)\tau (n) denote the number of positive integer divisors of nn. Find the sum of the six least positive integers nn that are solutions to τ(n)+τ(n+1)=7\tau (n) + \tau (n+1) = 7.
2019 AIME IAIMEAIME Inumber theory
Pretty Numbers

Source: 2019 AIME ii #9

3/22/2019
Call a positive integer nn kk-pretty if nn has exactly kk positive divisors and nn is divisible by kk. For example, 1818 is 66-pretty. Let SS be the sum of positive integers less than 20192019 that are 2020-pretty. Find S20\tfrac{S}{20}.
AMCAIMEAIME II2019 AIME II2019 AMCDivisors