Divisor Sum Calculator

About this calculator

The divisor sum function, σ(n), adds up every positive divisor of an integer n, including 1 and n itself — for example, σ(12) = 1+2+3+4+6+12 = 28. It's a foundational function in elementary number theory, alongside the related divisor-count function τ(n).

σ(n) is central to classifying numbers by how their divisors compare to n itself: a perfect number satisfies σ(n) = 2n (like 6 or 28), an abundant number has σ(n) > 2n, and a deficient number has σ(n) < 2n. This calculator returns both σ(n) and the count of divisors for any positive integer.