MathDB
Putnam 1961 A4

Source: Putnam 1961

June 5, 2022
PutnamArithmetic Functionsnumber theory

Problem Statement

Let Ω(n)\Omega(n) be the number of prime factors of nn. Define f(1)=1f(1)=1 and f(n)=(−1)Ω(n).f(n)=(-1)^{\Omega(n)}. Furthermore, let F(n)=∑d∣nf(d).F(n)=\sum_{d|n} f(d). Prove that F(n)=0,1F(n)=0,1 for all positive integers nn. For which integers nn is F(n)=1?F(n)=1?
Back to ProblemsView on AoPS