factorize

factorize.cs

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;

const int N = 120;

var kvpString = factorize(N).Select(kvp => $"{kvp.Key}: {kvp.Value}");
Console.WriteLine($"[{String.Join(", ", kvpString)}]");

Multiset<int> factorize(int n)
{
    var factors = new Multiset<int>();

    for (var divisor = 2; divisor * divisor <= n; divisor++)
    {
        while (n % divisor == 0)
        {
            n /= divisor;
            factors.Push(divisor);
        }
    }

    if (n != 1) factors.Push(n);

    return factors;
}

class Multiset<T> : IEnumerable<KeyValuePair<T, int>>
{
    private SortedDictionary<T, int> dictionary = new();

    public int this[T key] => dictionary.ContainsKey(key) ? dictionary[key] : 0;

    public void Push(T value)
    {
        if (dictionary.ContainsKey(value))
        {
            dictionary[value]++;
        }
        else
        {
            dictionary[value] = 1;
        }
    }

    public IEnumerator<KeyValuePair<T, int>> GetEnumerator() => dictionary.GetEnumerator();
    IEnumerator IEnumerable.GetEnumerator() => dictionary.GetEnumerator();
}