gen-explain-the-divisor-function-as-you-would-to-a-capable-stude-3c95

Explain the divisor function as you would to a capable student, in 3-4 sentences.

The divisor function, denoted σ(n) or σ₁(n), gives you the sum of all positive divisors of a number n, including 1 and n itself. For example, σ(6) = 1 + 2 + 3 + 6 = 12, since those are all the numbers that divide evenly into 6. There's also a related function τ(n) (or σ₀(n)) that simply counts how many divisors n has rather than summing them. These functions are multiplicative, meaning if two numbers are coprime (share no common factors), the divisor function of their product equals the product of their divisor functions: σ(mn) = σ(m)·σ(n) when gcd(m,n) = 1.