Add all positive divisors of a nonzero integer using its prime-power structure. Beside sum of divisors, the output shows the operation used to obtain it.
The sum-of-divisors function multiplies geometric sums 1+p+…+p^a for each prime power p^a in the factorization.
Read Sum of divisors against Nonzero integer, not in isolation. Use the fixed condition to estimate the Divisor Sum magnitude. When the fixed condition is altered, label the new Divisor Sum trial. Its Sum of divisors should not replace the original Divisor Sum answer.
Proper-divisor sums classify perfect, abundant, and deficient numbers and appear in multiplicative number theory. A related application of Divisor Sum is inspect the divisors.
For 28 = 2²×7, the divisor sum is (1+2+4)(1+7)=56. Its proper divisors therefore sum to 56−28=28.
Factor n, form one finite geometric sum for each distinct prime, multiply the sums, and subtract n only when proper divisors are requested. To continue from Divisor Sum, try perfect-number test.
This result includes the input itself. Zero is excluded, and negative signs do not alter the positive-divisor set.
Subtracting the original number converts the displayed total into a proper-divisor sum. Comparing that value with the input produces three classifications: deficient when smaller, perfect when equal, and abundant when larger. State whether the input itself was included whenever the sum is quoted.
Keep Nonzero integer integral when Divisor Sum requires integers. Verify the result through the defining Divisor Sum identity.
Test zero in Divisor Sum, then test one in Divisor Sum. Rebuild the starting integer through Divisor Sum.
Choose a nearby Nonzero integer whose effect on Sum of divisors is easy to anticipate. With the fixed condition held constant, the Divisor Sum result should move in the expected direction. This controlled Divisor Sum comparison is more revealing than several simultaneous edits.
Units and conventions belong with a Divisor Sum answer. Confirm that Nonzero integer and the fixed condition use the intended interpretation, then label Sum of divisors the same way. A numerically correct Sum of divisors can still answer the wrong Divisor Sum question when that context changes.
Yes.
Subtract the positive input from the displayed total.
It is 1.
Yes for coprime factors.