Collected Prime Factorization and Multiplicative Functions
a) State a formula for tau (n), the number of divisions of n, in terms of the collected prime factorization of n.
b) define the term multiplicative function.
c) Suppose that f and g are multiplicative functions. Prove that the function h defined by
h(n) = SUM (d|n) f(d)*g(n/d) is also multiplicative.
d) Find a formula for q(n) in terms of the collected prime factorization for n, where
q(n) = SUM (d/n) tau(d).
e) Find the smallest positive solution to q(n) = 45.