MathDB

For positive integers

n

, let

f_2(n)

denote the number of divisors of

n

which are perfect squares, and

f_3(n)

denotes the number of positive divisors which are perfect cubes. Prove that for each positive integer

k

there exists a positive integer

n

for which

\frac{f_2(n)}{f_3(n)}=k

Problem Statement