MathDB

The popularity of a positive integer

n

is the number of positive integer divisors of

n

. For example,

1

has popularity

1

, and

12

has popularity

6

. For each number

n

between

1

and

30

inclusive, Cathy writes the number

n

k

pieces of paper, where

k

is the popularity of

n

. Cathy then picks a piece of paper at random. Compute the probability that she will pick an even integer.

Problem Statement