Code Room
CodingMediumcod-g844
Subject Number theoryLevel Mid–Senior~20 minCommon in Algorithms & data structures interviewsIndustries Software development

Question

Return the number of positive divisors of n (the divisor-count function tau(n)), for n up to about 10^12. Counting by looping to n is far too slow; instead factorize n by trial division up to sqrt(n), and use that if n = product of p_i^e_i, then tau(n) = product of (e_i + 1). Return 0 for n <= 0.

Implement
count_divisors(n: int) → int
Examples
in[12]out6
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.

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.