Method and source check
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Editorial check of method and sources; this is not professional review or advice.
Method
The calculator accepts an integer from 2 through 999,999,999,999. It repeatedly divides by 2 and then by odd candidates up to the square root of the remaining value, producing the prime powers, positive divisors, divisor count, and divisor sum.
n = ∏pᵢᵃⁱ
d(n) = ∏(aᵢ + 1)
σ(n) = ∏((pᵢ^(aᵢ + 1) − 1) / (pᵢ − 1))
Variables and units
- pᵢ
- a distinct prime factor
- aᵢ
- the exponent of that prime factor
- d(n) / σ(n)
- number / sum of positive divisors
Worked example
360 = 2³ × 3² × 5. It has (3 + 1)(2 + 1)(1 + 1) = 24 positive divisors, whose sum is 15 × 13 × 6 = 1,170.
Limitations
Prime factors, exponents, divisor count, and divisors are exact integers for accepted inputs; the divisor sum is displayed as a whole number. No decimal precision or trailing-zero formatting is applied.
- Only positive integers in the displayed range are accepted. Trial division can take longer for large prime inputs near the upper limit; the result does not constitute a cryptographic primality certificate.
- Input 360 returns 2³ × 3² × 5, 24 positive divisors, divisor sum 1,170, and isPrime false.
- Input 13 returns prime factor 13, two positive divisors [1, 13], divisor sum 14, and isPrime true.
- Inputs below 2, above 999,999,999,999, or with a fractional part fail validation; the form accepts integers only.