MathDB
2021 Algebra/NT #5: Phi summation

Source:

May 30, 2021
Summationalgebranumber theory

Problem Statement

Let nn be the product of the first 1010 primes, and let S=∑xy∣nφ(x)⋅y,S=\sum_{xy\mid n} \varphi(x) \cdot y, where φ(x)\varphi(x) denotes the number of positive integers less than or equal to xx that are relatively prime to xx, and the sum is taken over ordered pairs (x,y)(x, y) of positive integers for which xyxy divides nn. Compute Sn.\tfrac{S}{n}.
Back to ProblemsView on AoPS