The Erdös discrepancy problem over the squarefree and cubefree integers

A question of Erdös, known as the Erdös discrepancy problem, asks if any arithmetic sequence of +-1 has infinite discrepancy. This has became a Theorem by T. Tao in 2015. A key step in its proof was to show that a completely multiplicative function assuming only +-1 values has unbounded partial sums. In this talk I will consider similar questions for multiplicative functions supported on the squarefree and cubefree integers.