Smallest Value After Replacing With Sum of Prime Factors — LeetCode 2507 Python Solution

MediumMathNumber TheorySimulation
Problem
#2507
Reading time
3 min

The problem

You are given a positive integer n. Continuously replace n with the sum of its prime factors.

Example

Input
n = 15
Output
5
Explanation
Initially, n = 15.

Python solution

Python
class Solution:
    def smallestValue(self, n: int) -> int:
        while 1:
            t, s, i = n, 0, 2
            while i <= n // i:
                while n % i == 0:
                    n //= i
                    s += i
                i += 1
            if n > 1:
                s += n
            if s == t:
                return t
            n = s

Complexity

MeasureComplexity
TimeO(\sqrt{n})
SpaceO(1) auxiliary

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 2507. Smallest Value After Replacing With Sum of Prime Factors is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math and Number Theory.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

Related problems

Frequently asked questions

How hard is LeetCode 2507. Smallest Value After Replacing With Sum of Prime Factors?
LeetCode 2507. Smallest Value After Replacing With Sum of Prime Factors is rated Medium on LeetCode.
What is the time complexity of LeetCode 2507. Smallest Value After Replacing With Sum of Prime Factors?
The Python solution on this page runs in O(\sqrt{n}).
What is the space complexity of LeetCode 2507. Smallest Value After Replacing With Sum of Prime Factors?
The Python solution on this page uses O(1) auxiliary space.
What topics does LeetCode 2507. Smallest Value After Replacing With Sum of Prime Factors cover?
LeetCode 2507. Smallest Value After Replacing With Sum of Prime Factors is tagged Math, Number Theory and Simulation on LeetCode.

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