MathDB

To every natural number

k, k \geq 2

, there corresponds a sequence

a_n(k)

according to the following rule: a_0 = k, \qquad a_n = \tau(a_{n-1}) \forall n \geq 1, in which

\tau(a)

is the number of different divisors of

a

. Find all

k

for which the sequence

a_n(k)

does not contain the square of an integer.

Problem Statement