CodingMediumcod-g825

Subject Number theoryLevel Mid–Senior~20 minCommon in Algorithms & data structures interviewsIndustries Software development

Question

Compute sigma(n), the sum of all positive divisors of n (including 1 and n itself), for a single positive integer n up to about 10^12. A loop to n is far too slow; instead factorize n by trial division up to sqrt(n) and use the multiplicative product formula for sigma over prime powers. Return 0 for n <= 0.

Implement

sum_of_divisors(n: int) → int

Examples

in[12]out28

What a strong answer looks like

State your approach and its time/space complexity out loud before you optimize. Handle the edge cases (empty input, duplicates, overflow), and say why you chose this over the brute force. Green tests are the floor, not the grade.

Learn the concepts

Vibe coding: describe the solution in plain language (or narrate it) and the coach grades your approach. Generating runnable code from your description is coming next.

Run or narrate your approach, then ask the coach.