gen-define-the-divisor-function-and-give-one-short-worked-exampl-f27f

Define the divisor function and give one short worked example.

# Divisor Function The **divisor function** σ(n) is defined as the sum of all positive divisors of a positive integer n. **Formal definition:** $$\sigma(n) = \sum_{d|n} d$$ where the sum is taken over all positive divisors d of n. ## Worked Example Find σ(12). **Solution:** First, list all positive divisors of 12: - 1, 2, 3, 4, 6, 12 Then sum them: $$\sigma(12) = 1 + 2 + 3 + 4 + 6 + 12 = 28$$ --- **Note:** Sometimes σₖ(n) denotes the sum of the k-th powers of divisors, where σ₁(n) = σ(n) is the standard divisor function, and σ₀(n) counts the number of divisors.