The question is:
Develop a formula for $\delta_2(n)$, the sum of the squares of the positive divisors of $n$.
The question is:
Develop a formula for $\delta_2(n)$, the sum of the squares of the positive divisors of $n$.
Hopefully, this can help. Let's say you wanted to find the sum of the positive divisors of $180=2^2\times3^2\times5$. The sum can be written as
$(1+2^1+2^2)(1+3^1+3^2)(1+5)$
Since each of the factors is a geometric series, this can be rewritten as
$\dfrac{2^3-1}{2-1}\times\dfrac{3^3-1}{3-1}\times\dfrac{5^2-1}{5-1}$
Can you see how to alter this method for $\delta_2(180)?$
Hint: prove it's multiplicative, then evaluate it on prime powers.