IR-TST 2013 Problem 15

a) Does there exist a sequence $a_1<a_2<\dots$ of positive integers, such that there is a positive integer $N$ that $\forall m>N$ , $a_m$ has exactly $d(m)-1$ divisors among $a_i$ s?

b) Does there exist a sequence $a_1<a_2<\dots$ of positive integers, such that there is a positive integer $N$ that $\forall m>N$ , $a_m$ has exactly $d(m)+1$ divisors among $a_i$ s?