For any positive integer $n $ let $ d(n) $ denote the number of positive divisors of $ n $. Do there exist positive integers $ a $ and $b $, such that $ d(a)=d(b)$ and $ d(a^2 ) = d(b^2 ) $, but $ d(a^3 ) \ne d(b^3 ) $ ?
Problem
Source: Middle European Mathematical Olympiad 2012 - Team Compt. T-8
Tags: number theory proposed, number theory