How does one show that the sigma function (the sum of all the positive divisors of an integer) is multiplicative?
i.e. s(p×q)=s(p)×s(q) where p and q are coprime.

s(p^a n)=s(p^a)s(n)

where p is a prime and n is coprime to p.

But if b|n, then pⁱ b|p^a n, where 0 £ i £ a, and if we have a list of positive divisors of n as b₁, b₂, ..., b_m

then {pⁱb_j:0 £ i £ a, 1 £ j £ m} are distinct and are the only divisors of p^a n. Hence sigma function is multiplicative.

Kerwin