To every natural number k,k≥2, there corresponds a sequence an(k) according to the following rule:
a_0 = k, \qquad a_n = \tau(a_{n-1}) \forall n \geq 1,
in which τ(a) is the number of different divisors of a. Find all k for which the sequence an(k) does not contain the square of an integer. number theoryprime factorizationalgebra proposedalgebra