Pairing Up Integer Divisors/Factors

Explanations 2

• Oftentimes, it is useful to think of factors in pairs. The best way to illustrate this is swith an example. Let τ(n)\tau(n)τ(n) be the number of divisor of nnn. Prove that ∏d∣n,…

  By Jason Chen

• Let σ(n)\sigma(n)σ(n) be sum of divisors of nnn, τ(n)\tau(n)τ(n) be number of divisor of nnn. Prove that for: (a) Any n≥7n \ge 7n≥7 then σ(n)<nln⁡n\sigma(n)<n \ln nσ(n)<nlnn. (b…

  By Toan Pham