Sum of Divisors Calculator

About this calculator

The sigma function, written σ(n), sums every positive divisor of a whole number n, including 1 and n itself, so σ(6) = 1 + 2 + 3 + 6 = 12. Subtracting n from that total gives the aliquot sum, the sum of n's divisors excluding n itself, a distinction that dates back to ancient Greek number theory and Euclid's study of what he called perfect numbers.

A number is classified as perfect when its aliquot sum equals the number itself (6 and 28 are the first two), abundant when the aliquot sum exceeds the number, and deficient when it falls short, classifications still used today in recreational and elementary number theory, and the sigma function itself reappears in more advanced settings such as the study of amicable number pairs and certain primality-related cryptographic computations.

Enter a whole number and this calculator returns the sum of all its positive divisors along with its aliquot sum and classification.