Sum of Positive Divisors Calculator

Factor n and multiply the finite geometric sum for each prime power. This sigma convention includes n itself; the separate proper-divisor metric does not. Inputs must be whole numbers inside the displayed safe bound. The calculator does not round decimals into the domain or silently substitute a different convention, so verify each entered integer before interpreting the exact result.

The total includes one and n. The proper-divisor metric subtracts n before assigning the number class. For n = 12, directly adding 1, 2, 3, 4, 6, and 12 confirms the product result. Use the displayed factors, recurrence step, or modular residue as an independent check. Exact integer output means the implemented arithmetic has no decimal approximation within its bound; it does not prove an unrelated theorem or an unstated combinatorial model.

The input cap prevents factorization stalls and keeps the displayed divisor sums within the supported exact range. The classification is arithmetic terminology and does not assess quality, randomness, or cryptographic suitability. The bound keeps browser work predictable and every returned integer within JavaScript's exact safe range. Larger inputs need arbitrary-precision software, explicit resource controls, and independent verification rather than treating an overflowed floating-point value as exact.