Let tau(n) = # of pos odd divisors of n

Let sigma(n) = sum of pos. odd divisors of n

Note that tau and sigma are both multiplicative functions.

1.) Evaluate the following:

tau(12)

tau(16)

sigma(12)

sigma(16)

2.) Let n = p_(1)^(a_1)*p_(2)^(a_2)*p_(3)^(a_3)* ... *p_(k)^(a_k)

a.) Determine a formula for tau(n) in terms of the p's and a's.

b.) Determine a formula for sigma in terms of the p's and a's