2026-07-21：可由多种立方和构造的整数。用go语言，给定一个正整数上限 n，一个正整数 x 被称为“好整数”，当且仅当它可以表示为两组不

package main

import (
    "fmt"
    "slices"
    "sort"
)

var goodIntegers []int// 1554 个

func init() {
    const mx = 1_000_000_000
    cnt := map[int]int{}
    for a := 1; a*a*a <= mx/2; a++ {
        for b := a; a*a*a+b*b*b <= mx; b++ {
            cnt[a*a*a+b*b*b]++
        }
    }

    for x, c := range cnt {
        if c > 1 {
            goodIntegers = append(goodIntegers, x)
        }
    }

    slices.Sort(goodIntegers)
}

func findGoodIntegers(n int) []int {
    i := sort.SearchInts(goodIntegers, n+1)
    return goodIntegers[:i]
}

func main() {
    n := 4104
    result := findGoodIntegers(n)
    fmt.Println(result)
}

# -*-coding:utf-8-*-

def init_good_integers():
    """初始化好整数列表，这些数可以用至少两种方式表示为两个立方数之和"""
    mx = 1_000_000_000
    cnt = {}
    
    a = 1
    while a * a * a <= mx // 2:
        b = a
        while a * a * a + b * b * b <= mx:
            val = a * a * a + b * b * b
            cnt[val] = cnt.get(val, 0) + 1
            b += 1
        a += 1
    
    good_integers = []
    for x, c in cnt.items():
        if c > 1:
            good_integers.append(x)
    
    good_integers.sort()
    return good_integers


def find_good_integers(n, good_integers):
    """返回所有不大于 n 的好整数"""
    result = []
    for x in good_integers:
        if x <= n:
            result.append(x)
        else:
            break
    return result


def main():
    good_integers = init_good_integers()
    
    n = 4104
    result = find_good_integers(n, good_integers)
    print(result)


if __name__ == "__main__":
    main()

#include <iostream>
#include <vector>
#include <unordered_map>
#include <algorithm>

using namespace std;

vector<int> goodIntegers;

// 全局初始化器
namespace {
struct InitGoodIntegers {
    InitGoodIntegers() {
        const int mx = 1'000'000'000;
        unordered_map<int, int> cnt;

        for (int a = 1; a * a * a <= mx / 2; a++) {
            for (int b = a; a * a * a + b * b * b <= mx; b++) {
                int val = a * a * a + b * b * b;
                cnt[val]++;
            }
        }

        for (const auto& [x, c] : cnt) {
            if (c > 1) {
                goodIntegers.push_back(x);
            }
        }

        sort(goodIntegers.begin(), goodIntegers.end());
    }
} initGoodIntegers;
}

vector<int> findGoodIntegers(int n) {
    auto it = upper_bound(goodIntegers.begin(), goodIntegers.end(), n);
    int idx = distance(goodIntegers.begin(), it);
    return vector<int>(goodIntegers.begin(), goodIntegers.begin() + idx);
}

int main() {
    int n = 4104;
    vector<int> result = findGoodIntegers(n);

    cout << "[";
    for (size_t i = 0; i < result.size(); i++) {
        cout << result[i];
        if (i < result.size() - 1) {
            cout << ", ";
        }
    }
    cout << "]" << endl;

    return 0;
}