MathDB

Pretty Numbers

Source: 2019 AIME ii #9

March 22, 2019

AMCAIMEAIME II2019 AIME II2019 AMCDivisors

Problem Statement

Call a positive integer

n

k

-pretty if

n

has exactly

k

positive divisors and

n

is divisible by

k

. For example,

18

is

6

-pretty. Let

S

be the sum of positive integers less than

2019

that are

20

-pretty. Find

\tfrac{S}{20}

.

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