Divisor Function Calculator

This divisor function calculator works out sigma of n, the sum of every positive divisor of a whole number, together with how many divisors it has and what those divisors add up to when you leave out the number itself. Divisors and their sums turn up throughout number theory, from testing whether a number is prime or composite to classifying it as perfect, abundant or deficient, and they follow neat formulas once you know a number's prime factorisation. You enter any whole number n from 1 up to one billion, and the calculator returns three figures at once: sigma of n, the total of all its divisors including 1 and n; the number of divisors it has; and the sum of its proper divisors, meaning every divisor except n itself. Large results are grouped with commas so they stay easy to read. Try the default value of 12 to see how it works: its divisors are 1, 2, 3, 4, 6 and 12, giving sigma(12) = 28, a divisor count of 6, and a proper divisor sum of 16, one short of 12 itself, which makes 12 an abundant number. Change the number and the results update immediately using an exact integer algorithm, so the figures stay precise even for large values. It is a handy tool for students, programmers and anyone curious about how a number's factors behave.

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