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Section 20.5 Looking Ahead

Let's recap.

  • The average value of τ(n) was log(n)+2γ1.

  • The average value of σ(n) was (12d=11d2)n.

    • Because of Euler's amazing solution to the Basel problem, we know that

      d=11d2=π26

      so the constant in question is π212.

We end with the question of yet another average value. What might happen with the ϕ function? You can try out various ideas in the following interact. Note that a is the coefficient and n is the power of a model axn.

Hopefully you started finding something interesting. However, we aren't ready to prove anything about this case quite – yet!