Soma dos Divisores (σ)

The Sum of Divisors (σ) calculator computes the sum of all positive divisors of a natural number n. For example, for n = 6, the divisors are 1, 2, 3, and 6, and the sum σ(6) = 12. This function is classic in number theory and appears in divisibility problems and perfect numbers.

The operation is simple: enter a positive integer and the tool finds all its divisors, summing them. The formula σ(n) = Σ d|n d is implemented by an efficient algorithm that tests divisors up to the square root of n. The result is displayed along with the list of divisors, when applicable.

Use this calculator to check if a number is perfect (σ(n) = 2n), deficient (σ(n) < 2n), or abundant (σ(n) > 2n). It is also useful in school math problems, contests, and studies of numerical sequences. For example, numbers like 6, 28, and 496 are perfect because the sum of their divisors (excluding the number itself) equals the number.

Caveats: the sum includes the number itself. For the sum of proper divisors (function s(n) = σ(n) - n), subtract n manually. Also, the tool works only for positive integers. Avoid very large numbers (above 10^9) to prevent processing overload.