论坛 › 刨根究底 › 有这样一串数(OEIS找不到)

王守恩 发表于 2024-4-23 12:55:41

有这样一串数(OEIS找不到)

有这样一串数。

T(1)=6, 1*6=2*3,

T(2)=48, 1*4*12=2*3*8,

T(3)=240, 1*4*6*10=2*3*5*8,

T(4)=3360, 1*4*6*10*14=2*3*5*7*16,

T(5)=30240,1*4*6*9*10*14=2*3*5*7*8*18,
......

2n个不同的正整数,n个数的积=n个数的积。我们希望：积是最小的。

应该有这一串数：蛮有规律的呀？可是为什么OEIS找不到，

肯定是哪里错了？谢谢各位！

northwolves 发表于 2024-5-9 21:37:33

For n=13, 62768369664000={1, 2, 3, 4, 11, 21, 24, 25, 26, 27, 28, 30, 32}{5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 18, 20, 22}

northwolves 发表于 7 天前

n=10

2032933777875        {1,3,5,7,33,45,51,57,65,69}        {9,11,13,15,17,19,21,23,25,27}
2032933777875        {1,3,5,11,21,45,51,57,65,69}        {7,9,13,15,17,19,23,25,27,33}
2032933777875        {1,3,5,15,21,33,51,57,65,69}        {7,9,11,13,17,19,23,25,27,45}
2032933777875        {1,3,5,17,21,33,45,57,65,69}        {7,9,11,13,15,19,23,25,27,51}
2032933777875        {1,3,5,19,21,33,45,51,65,69}        {7,9,11,13,15,17,23,25,27,57}
2032933777875        {1,3,5,21,23,33,45,51,57,65}        {7,9,11,13,15,17,19,25,27,69}
2032933777875        {1,3,7,9,25,33,51,57,65,69}        {5,11,13,15,17,19,21,23,27,45}
2032933777875        {1,3,7,11,15,45,51,57,65,69}        {5,9,13,17,19,21,23,25,27,33}
2032933777875        {1,3,7,11,25,27,51,57,65,69}        {5,9,13,15,17,19,21,23,33,45}
2032933777875        {1,3,7,13,25,33,45,51,57,69}        {5,9,11,15,17,19,21,23,27,65}
2032933777875        {1,3,7,15,17,33,45,57,65,69}        {5,9,11,13,19,21,23,25,27,51}
2032933777875        {1,3,7,15,19,33,45,51,65,69}        {5,9,11,13,17,21,23,25,27,57}
2032933777875        {1,3,7,15,23,33,45,51,57,65}        {5,9,11,13,17,19,21,25,27,69}
2032933777875        {1,3,7,17,25,27,33,57,65,69}        {5,9,11,13,15,19,21,23,45,51}
2032933777875        {1,3,7,19,25,27,33,51,65,69}        {5,9,11,13,15,17,21,23,45,57}
2032933777875        {1,3,7,23,25,27,33,51,57,65}        {5,9,11,13,15,17,19,21,45,69}
2032933777875        {1,3,9,11,21,25,51,57,65,69}        {5,7,13,15,17,19,23,27,33,45}
2032933777875        {1,3,9,17,21,25,33,57,65,69}        {5,7,11,13,15,19,23,27,45,51}
2032933777875        {1,3,9,19,21,25,33,51,65,69}        {5,7,11,13,15,17,23,27,45,57}
2032933777875        {1,3,9,21,23,25,33,51,57,65}        {5,7,11,13,15,17,19,27,45,69}
2032933777875        {1,3,11,13,21,25,45,51,57,69}        {5,7,9,15,17,19,23,27,33,65}
2032933777875        {1,3,11,15,17,21,45,57,65,69}        {5,7,9,13,19,23,25,27,33,51}
2032933777875        {1,3,11,15,19,21,45,51,65,69}        {5,7,9,13,17,23,25,27,33,57}
2032933777875        {1,3,11,15,21,23,45,51,57,65}        {5,7,9,13,17,19,25,27,33,69}
2032933777875        {1,3,11,17,21,25,27,57,65,69}        {5,7,9,13,15,19,23,33,45,51}
2032933777875        {1,3,11,19,21,25,27,51,65,69}        {5,7,9,13,15,17,23,33,45,57}
2032933777875        {1,3,11,21,23,25,27,51,57,65}        {5,7,9,13,15,17,19,33,45,69}
2032933777875        {1,3,13,15,21,25,33,51,57,69}        {5,7,9,11,17,19,23,27,45,65}
2032933777875        {1,3,13,17,21,25,33,45,57,69}        {5,7,9,11,15,19,23,27,51,65}
2032933777875        {1,3,13,19,21,25,33,45,51,69}        {5,7,9,11,15,17,23,27,57,65}
2032933777875        {1,3,13,21,23,25,33,45,51,57}        {5,7,9,11,15,17,19,27,65,69}
2032933777875        {1,3,15,17,19,21,33,45,65,69}        {5,7,9,11,13,23,25,27,51,57}
2032933777875        {1,3,15,17,21,23,33,45,57,65}        {5,7,9,11,13,19,25,27,51,69}
2032933777875        {1,3,15,19,21,23,33,45,51,65}        {5,7,9,11,13,17,25,27,57,69}
2032933777875        {1,3,17,19,21,25,27,33,65,69}        {5,7,9,11,13,15,23,45,51,57}
2032933777875        {1,3,17,21,23,25,27,33,57,65}        {5,7,9,11,13,15,19,45,51,69}
2032933777875        {1,3,19,21,23,25,27,33,51,65}        {5,7,9,11,13,15,17,45,57,69}
2032933777875        {1,5,7,9,11,45,51,57,65,69}        {3,13,15,17,19,21,23,25,27,33}
2032933777875        {1,5,7,9,15,33,51,57,65,69}        {3,11,13,17,19,21,23,25,27,45}
2032933777875        {1,5,7,9,17,33,45,57,65,69}        {3,11,13,15,19,21,23,25,27,51}
2032933777875        {1,5,7,9,19,33,45,51,65,69}        {3,11,13,15,17,21,23,25,27,57}
2032933777875        {1,5,7,9,23,33,45,51,57,65}        {3,11,13,15,17,19,21,25,27,69}
2032933777875        {1,5,7,11,15,27,51,57,65,69}        {3,9,13,17,19,21,23,25,33,45}
2032933777875        {1,5,7,11,17,27,45,57,65,69}        {3,9,13,15,19,21,23,25,33,51}
2032933777875        {1,5,7,11,19,27,45,51,65,69}        {3,9,13,15,17,21,23,25,33,57}
2032933777875        {1,5,7,11,23,27,45,51,57,65}        {3,9,13,15,17,19,21,25,33,69}
2032933777875        {1,5,7,13,15,33,45,51,57,69}        {3,9,11,17,19,21,23,25,27,65}
2032933777875        {1,5,7,13,25,27,33,51,57,69}        {3,9,11,15,17,19,21,23,45,65}
2032933777875        {1,5,7,15,17,27,33,57,65,69}        {3,9,11,13,19,21,23,25,45,51}
2032933777875        {1,5,7,15,19,27,33,51,65,69}        {3,9,11,13,17,21,23,25,45,57}
2032933777875        {1,5,7,15,23,27,33,51,57,65}        {3,9,11,13,17,19,21,25,45,69}
2032933777875        {1,5,7,17,19,27,33,45,65,69}        {3,9,11,13,15,21,23,25,51,57}
2032933777875        {1,5,7,17,23,27,33,45,57,65}        {3,9,11,13,15,19,21,25,51,69}
2032933777875        {1,5,7,19,23,27,33,45,51,65}        {3,9,11,13,15,17,21,25,57,69}
2032933777875        {1,5,9,11,15,21,51,57,65,69}        {3,7,13,17,19,23,25,27,33,45}
2032933777875        {1,5,9,11,17,21,45,57,65,69}        {3,7,13,15,19,23,25,27,33,51}
2032933777875        {1,5,9,11,19,21,45,51,65,69}        {3,7,13,15,17,23,25,27,33,57}
2032933777875        {1,5,9,11,21,23,45,51,57,65}        {3,7,13,15,17,19,25,27,33,69}
2032933777875        {1,5,9,13,21,25,33,51,57,69}        {3,7,11,15,17,19,23,27,45,65}
2032933777875        {1,5,9,15,17,21,33,57,65,69}        {3,7,11,13,19,23,25,27,45,51}
2032933777875        {1,5,9,15,19,21,33,51,65,69}        {3,7,11,13,17,23,25,27,45,57}
2032933777875        {1,5,9,15,21,23,33,51,57,65}        {3,7,11,13,17,19,25,27,45,69}
2032933777875        {1,5,9,17,19,21,33,45,65,69}        {3,7,11,13,15,23,25,27,51,57}
2032933777875        {1,5,9,17,21,23,33,45,57,65}        {3,7,11,13,15,19,25,27,51,69}
2032933777875        {1,5,9,19,21,23,33,45,51,65}        {3,7,11,13,15,17,25,27,57,69}
2032933777875        {1,5,11,13,15,21,45,51,57,69}        {3,7,9,17,19,23,25,27,33,65}
2032933777875        {1,5,11,13,21,25,27,51,57,69}        {3,7,9,15,17,19,23,33,45,65}
2032933777875        {1,5,11,15,17,21,27,57,65,69}        {3,7,9,13,19,23,25,33,45,51}
2032933777875        {1,5,11,15,19,21,27,51,65,69}        {3,7,9,13,17,23,25,33,45,57}
2032933777875        {1,5,11,15,21,23,27,51,57,65}        {3,7,9,13,17,19,25,33,45,69}
2032933777875        {1,5,11,17,19,21,27,45,65,69}        {3,7,9,13,15,23,25,33,51,57}
2032933777875        {1,5,11,17,21,23,27,45,57,65}        {3,7,9,13,15,19,25,33,51,69}
2032933777875        {1,5,11,19,21,23,27,45,51,65}        {3,7,9,13,15,17,25,33,57,69}
2032933777875        {1,5,13,15,17,21,33,45,57,69}        {3,7,9,11,19,23,25,27,51,65}
2032933777875        {1,5,13,15,19,21,33,45,51,69}        {3,7,9,11,17,23,25,27,57,65}
2032933777875        {1,5,13,15,21,23,33,45,51,57}        {3,7,9,11,17,19,25,27,65,69}
2032933777875        {1,5,13,17,21,25,27,33,57,69}        {3,7,9,11,15,19,23,45,51,65}
2032933777875        {1,5,13,19,21,25,27,33,51,69}        {3,7,9,11,15,17,23,45,57,65}
2032933777875        {1,5,13,21,23,25,27,33,51,57}        {3,7,9,11,15,17,19,45,65,69}
2032933777875        {1,5,15,17,19,21,27,33,65,69}        {3,7,9,11,13,23,25,45,51,57}
2032933777875        {1,5,15,17,21,23,27,33,57,65}        {3,7,9,11,13,19,25,45,51,69}
2032933777875        {1,5,15,19,21,23,27,33,51,65}        {3,7,9,11,13,17,25,45,57,69}
2032933777875        {1,5,17,19,21,23,27,33,45,65}        {3,7,9,11,13,15,25,51,57,69}
2032933777875        {1,7,9,11,13,25,45,51,57,69}        {3,5,15,17,19,21,23,27,33,65}
2032933777875        {1,7,9,11,15,17,45,57,65,69}        {3,5,13,19,21,23,25,27,33,51}
2032933777875        {1,7,9,11,15,19,45,51,65,69}        {3,5,13,17,21,23,25,27,33,57}
2032933777875        {1,7,9,11,15,23,45,51,57,65}        {3,5,13,17,19,21,25,27,33,69}
2032933777875        {1,7,9,11,17,25,27,57,65,69}        {3,5,13,15,19,21,23,33,45,51}
2032933777875        {1,7,9,11,19,25,27,51,65,69}        {3,5,13,15,17,21,23,33,45,57}
2032933777875        {1,7,9,11,23,25,27,51,57,65}        {3,5,13,15,17,19,21,33,45,69}
2032933777875        {1,7,9,13,15,25,33,51,57,69}        {3,5,11,17,19,21,23,27,45,65}
2032933777875        {1,7,9,13,17,25,33,45,57,69}        {3,5,11,15,19,21,23,27,51,65}
2032933777875        {1,7,9,13,19,25,33,45,51,69}        {3,5,11,15,17,21,23,27,57,65}
2032933777875        {1,7,9,13,23,25,33,45,51,57}        {3,5,11,15,17,19,21,27,65,69}
2032933777875        {1,7,9,15,17,19,33,45,65,69}        {3,5,11,13,21,23,25,27,51,57}
2032933777875        {1,7,9,15,17,23,33,45,57,65}        {3,5,11,13,19,21,25,27,51,69}
2032933777875        {1,7,9,15,19,23,33,45,51,65}        {3,5,11,13,17,21,25,27,57,69}
2032933777875        {1,7,9,17,19,25,27,33,65,69}        {3,5,11,13,15,21,23,45,51,57}
2032933777875        {1,7,9,17,23,25,27,33,57,65}        {3,5,11,13,15,19,21,45,51,69}
2032933777875        {1,7,9,19,23,25,27,33,51,65}        {3,5,11,13,15,17,21,45,57,69}
2032933777875        {1,7,11,13,15,25,27,51,57,69}        {3,5,9,17,19,21,23,33,45,65}
2032933777875        {1,7,11,13,17,25,27,45,57,69}        {3,5,9,15,19,21,23,33,51,65}
2032933777875        {1,7,11,13,19,25,27,45,51,69}        {3,5,9,15,17,21,23,33,57,65}
2032933777875        {1,7,11,13,23,25,27,45,51,57}        {3,5,9,15,17,19,21,33,65,69}
2032933777875        {1,7,11,15,17,19,27,45,65,69}        {3,5,9,13,21,23,25,33,51,57}
2032933777875        {1,7,11,15,17,23,27,45,57,65}        {3,5,9,13,19,21,25,33,51,69}
2032933777875        {1,7,11,15,19,23,27,45,51,65}        {3,5,9,13,17,21,25,33,57,69}
2032933777875        {1,7,13,15,17,25,27,33,57,69}        {3,5,9,11,19,21,23,45,51,65}
2032933777875        {1,7,13,15,19,25,27,33,51,69}        {3,5,9,11,17,21,23,45,57,65}
2032933777875        {1,7,13,15,23,25,27,33,51,57}        {3,5,9,11,17,19,21,45,65,69}
2032933777875        {1,7,13,17,19,25,27,33,45,69}        {3,5,9,11,15,21,23,51,57,65}
2032933777875        {1,7,13,17,23,25,27,33,45,57}        {3,5,9,11,15,19,21,51,65,69}
2032933777875        {1,7,13,19,23,25,27,33,45,51}        {3,5,9,11,15,17,21,57,65,69}
2032933777875        {1,7,15,17,19,23,27,33,45,65}        {3,5,9,11,13,21,25,51,57,69}
2032933777875        {1,9,11,13,15,21,25,51,57,69}        {3,5,7,17,19,23,27,33,45,65}
2032933777875        {1,9,11,13,17,21,25,45,57,69}        {3,5,7,15,19,23,27,33,51,65}
2032933777875        {1,9,11,13,19,21,25,45,51,69}        {3,5,7,15,17,23,27,33,57,65}
2032933777875        {1,9,11,13,21,23,25,45,51,57}        {3,5,7,15,17,19,27,33,65,69}
2032933777875        {1,9,11,15,17,19,21,45,65,69}        {3,5,7,13,23,25,27,33,51,57}
2032933777875        {1,9,11,15,17,21,23,45,57,65}        {3,5,7,13,19,25,27,33,51,69}
2032933777875        {1,9,11,15,19,21,23,45,51,65}        {3,5,7,13,17,25,27,33,57,69}
2032933777875        {1,9,11,17,19,21,25,27,65,69}        {3,5,7,13,15,23,33,45,51,57}
2032933777875        {1,9,11,17,21,23,25,27,57,65}        {3,5,7,13,15,19,33,45,51,69}
2032933777875        {1,9,11,19,21,23,25,27,51,65}        {3,5,7,13,15,17,33,45,57,69}
2032933777875        {1,9,13,15,17,21,25,33,57,69}        {3,5,7,11,19,23,27,45,51,65}
2032933777875        {1,9,13,15,19,21,25,33,51,69}        {3,5,7,11,17,23,27,45,57,65}
2032933777875        {1,9,13,15,21,23,25,33,51,57}        {3,5,7,11,17,19,27,45,65,69}
2032933777875        {1,9,13,17,19,21,25,33,45,69}        {3,5,7,11,15,23,27,51,57,65}
2032933777875        {1,9,13,17,21,23,25,33,45,57}        {3,5,7,11,15,19,27,51,65,69}
2032933777875        {1,9,13,19,21,23,25,33,45,51}        {3,5,7,11,15,17,27,57,65,69}
2032933777875        {1,9,15,17,19,21,23,33,45,65}        {3,5,7,11,13,25,27,51,57,69}
2032933777875        {1,9,17,19,21,23,25,27,33,65}        {3,5,7,11,13,15,45,51,57,69}
2032933777875        {1,11,13,15,17,21,25,27,57,69}        {3,5,7,9,19,23,33,45,51,65}
2032933777875        {1,11,13,15,19,21,25,27,51,69}        {3,5,7,9,17,23,33,45,57,65}
2032933777875        {1,11,13,15,21,23,25,27,51,57}        {3,5,7,9,17,19,33,45,65,69}
2032933777875        {1,11,13,17,19,21,25,27,45,69}        {3,5,7,9,15,23,33,51,57,65}
2032933777875        {1,11,13,17,21,23,25,27,45,57}        {3,5,7,9,15,19,33,51,65,69}
2032933777875        {1,11,13,19,21,23,25,27,45,51}        {3,5,7,9,15,17,33,57,65,69}
2032933777875        {1,11,15,17,19,21,23,27,45,65}        {3,5,7,9,13,25,33,51,57,69}
2032933777875        {1,13,15,17,19,21,25,27,33,69}        {3,5,7,9,11,23,45,51,57,65}
2032933777875        {1,13,15,17,21,23,25,27,33,57}        {3,5,7,9,11,19,45,51,65,69}
2032933777875        {1,13,15,19,21,23,25,27,33,51}        {3,5,7,9,11,17,45,57,65,69}
2032933777875        {1,13,17,19,21,23,25,27,33,45}        {3,5,7,9,11,15,51,57,65,69}

mathe 发表于 7 天前

我们已经得出使用2N个不同的正整数得出的最小平方数的算数平方根，然后每个平方数可能会有多种正整数的组合选择。
而对于每个2N个正整数组合，划分成两组的方案也可能会有多组，我们可以计算一下它们的方案数目如下(A372794) , 使用动态规划的C++代码速度还不错，现在的主要限制在内存了:

N=2
6<1>
{ 1 2 3 6 }<1>

N=3
36<1>
{ 1 2 3 4 6 9 }<1>

N=4
240<1>
{ 1 2 3 4 5 6 8 10 }<3>

N=5
2520<1>
{ 1 2 3 4 5 6 7 9 10 14 }<4>

N=6
30240<3>
{ 1 2 3 4 5 6 7 8 9 12 14 15 }<10>
{ 1 2 3 4 5 6 7 8 9 10 14 18 }<11>
{ 1 2 3 4 5 6 7 8 9 10 12 21 }<10>

N=7
443520<1>
{ 1 2 3 4 5 6 7 8 9 10 11 14 16 22 }<15>

N=8
6652800<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 14 15 20 22 }<55>

N=9
133056000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 20 22 25 }<110>

N=10
2075673600<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 22 26 }<280>

N=11
58118860800<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 20 21 22 24 26 28 }<797>

N=12
1270312243200<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 22 24 26 27 34 }<1419>

N=13
29640619008000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 24 25 26 28 34 }<3557>

N=14
844757641728000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 25 26 27 28 34 38 }<5647>

N=15
25342729251840000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25 26 27 30 34 35 38 }<19559>

N=16
810967336058880000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25 26 27 28 30 32 34 38 40 }<59708>

N=17
27978373094031360000<3>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 30 32 34 35 36 38 46 }<115592>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 30 34 36 38 40 46 }<129320>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 30 32 34 38 45 46 }<115814>

N=18
1077167364120207360000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 30 33 34 35 38 42 44 46 }<346487>

N=19
43086694564808294400000<2>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 30 32 33 34 35 38 42 44 46 50 }<983805>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 30 32 33 34 35 38 40 42 46 55 }<1034227>

N=20
1499416970855328645120000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34 35 36 38 42 44 46 58 }<2106172>

N=21
74970848542766432256000000<2>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34 35 38 40 42 44 45 46 50 58 }<6618558>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34 35 36 38 40 42 46 50 55 58 }<6609936>

N=22
2788915565790911279923200000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 38 40 42 44 45 46 58 62 }<13994982>

N=23
140345428472058761183232000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34 35 36 38 39 40 42 44 45 46 48 50 52 58 }<65426469>

N=24
6090991595687350235352268800000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 38 39 40 42 44 45 46 48 49 52 58 62 }<110980446>

N=25
321952412914902798154334208000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 42 44 45 46 48 50 52 58 62 74 }<257148638>

N=26
18029335123234556696642715648000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 42 44 45 46 48 49 50 52 58 62 64 74 }<660593345>

N=27
1103395309541954869834534197657600000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 42 44 45 46 48 49 51 52 54 58 62 64 68 74 }<1966842579>

N=28
56549009614025187079019877629952000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 44 45 46 48 49 50 51 52 54 58 62 68 74 82 }<3909078573>

N=29
3641204521488451070453962852270080000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 42 44 45 46 48 49 50 51 52 54 55 58 60 62 64 66 68 74 }<20820932559>

N=30
204255022725858975729419797999386624000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 48 49 50 51 52 54 56 58 62 63 68 74 82 86 }<26864715089>

N=31
12540308372006225486643448063218155520000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 44 45 46 48 49 50 51 52 54 55 56 58 60 62 63 64 66 68 74 82 }<144689720443>

N=32
808849889994401543888502400077571031040000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 48 49 50 51 52 54 55 56 58 60 62 63 66 68 72 74 82 86 }<307476230099>

N=33
50687926439649163417012817071527784611840000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 54 55 56 58 60 62 63 64 66 68 74 82 86 94 }<571509614773>

N=34
3611514758825002893462163216346354653593600000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 54 55 56 57 58 60 62 63 66 68 74 75 76 82 86 94 }<1695094248112>

northwolves 发表于 2024-4-23 13:22:26

那是因为你从第2个就错了：
A354457        a(n) is the least integer for which there exist two disjoint sets of n positive integers each, all distinct, for which the product of the integers in either set is a(n).               

6, 36, 240, 2520, 30240, 443520, 6652800

From Jinyuan Wang, May 31 2022: (Start)
For n=2,       6 = 1*6                  = 2 * 3.
For n=3,      36 = 1*4*9                = 2 * 3 * 6.
For n=4,   240 = 1*3*8*10             = 2 * 4 * 5 * 6.
For n=5,    2520 = 1*2*9*10*14          = 3 * 4 * 5 * 6 * 7.
For n=6,   30240 = 1*2*6*10*14*18       = 3 * 4 * 5 * 7 * 8 * 9.
For n=7,443520 = 1*2*5*9*14*16*22   = 3 * 4 * 6 * 7 * 8 *10 *11.
For n=8, 6652800 = 1*2*3*12*14*15*20*22 = 4 * 5 * 6 * 7 * 8 * 9 *10 *11.

王守恩 发表于 2024-4-23 16:25:01

For n=2,       6 = 1*6                  = 2 * 3.
For n=3,      36 = 1*4*9                = 2 * 3 * 6.
For n=4,   240 = 1*3*8*10             = 2 * 4 * 5 * 6.
For n=5,    2520 = 1*2*9*10*14          = 3 * 4 * 5 * 6 * 7.
For n=6,   30240 = 1*2*6*10*14*18       = 3 * 4 * 5 * 7 * 8 * 9.
For n=7,443520 = 1*2*5*9*14*16*22   = 3 * 4 * 6 * 7 * 8 *10 *11.
For n=8, 6652800 = 1*2*3*12*14*15*20*22 = 4 * 5 * 6 * 7 * 8 * 9 *10 *11.
For n=9,               = 1*2*3*12*14*15*20*22*26 = 4 * 5 * 6 * 7 * 9 *10 *11*13*16.
For n=10,            = 1*2*3*12*14*15*20*22*26*34 = 4 * 5 * 6 * 7 *10 *11*13*16*17*18.
For n=11,               = 1*2*3*12*14*15*20*22*26*34*38 = 4 * 5 * 6 * 7 *10 *11*13*17*18*19*32.
......
至少这是一条路。

王守恩 发表于 2024-4-24 10:41:46

3种方法。

1, 添k,添2k, 减p,加2p(p是原有的数)。譬如：1*6=2*3, 添4,添8, 减6,加12, 1*4*12=2*3*8,
   当然, 添k,添3k, 减p,加3p,...都是可以的。

2, 约分。譬如：12/8=9/6,

3, 整体考虑。\(\sqrt{\frac{n!}{\ 若干个数相乘\ }}\)=正整数。譬如：\(\sqrt{\frac{10!}{\ 7*9\ }}\)=240。

王守恩 发表于 2024-5-9 18:46:58

A354457                a(n) is the least integer for which there exist two disjoint sets of n positive integers each, all distinct, for which the product of the integers in either set is a(n).       
       
6, 36, 240, 2520, 30240, 443520, 6652800 (list; graph; refs; listen; history; text; internal format)

For n=2,       6 = 1*6                = 2*3.
For n=3,      36 = 1*4*9            = 2*3*6.
For n=4,   240 = 1*3*8*10         = 2*4*5*6.
For n=5,    2520 = 1*2*9*10*14      = 3*4*5*6*7.
For n=6,   30240 = 1*2*6*10*14*18   = 3*4*5*7*8*9.
For n=7,443520 = 1*2*5*9*14*16*22    = 3*4*6*7*8*10*11.
For n=8, 6652800 = 1*2*3*12*14*15*20*22= 4*5*6*7*8*9*10*11.
......

a(7)-a(8)摘自 Jinyuan Wang——2022 年 5 月 31 日

我们动不了了吗？

northwolves 发表于 2024-5-9 21:03:18

For n=10, 4790016000= {1, 4, 5, 6, 9, 16, 21, 22, 24, 25}{2, 3, 8, 10, 11, 12, 14, 15, 18, 20}

northwolves 发表于 2024-5-9 21:13:09

For n=9, 958003200={2, 4, 6, 9, 10, 20, 21, 22, 24}{3, 5, 8, 11, 12, 14, 15, 16, 18}

northwolves 发表于 2024-5-9 21:20:55

For n=11,62270208000={1, 3, 5, 6, 8, 12, 21, 22, 24, 25, 26}{2, 4, 7, 9, 10, 11, 13, 15, 16, 18, 20}

northwolves 发表于 2024-5-9 21:25:35

For n=12, 2615348736000={1, 2, 3, 4, 20, 21, 22, 24, 25, 26, 27, 28}{5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18}

查看完整版本: 有这样一串数(OEIS找不到)