Compute 𝜏 (n) (tau function) for the following n values:
(a) 10
(b) 100
(c) 120
(d) 101
(a) The factors of 10 are $\{1, 2, 5, 10\}$.
Therefore $\tau (10) = 4$.
(b) The factors of 100 are $\{1, 2, 4, 5, 10, 20, 25, 50, 100\}$.
Therefore $\tau (100) = 9$.
(c) The factors of 120 are $\{1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120\}$.
Therefore $\tau (120) = 16$.
(d) The factors of 101 are $\{1, 101\}$.
Therefore $\tau (101) = 2$.