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# [求助] 有这样一串数(OEIS找不到)

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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。

 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}

### 评分

 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}

### 评分

 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>

### 评分

northwolves + 8 + 8 + 8 + 8 + 8 赞一个!

 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.

### 评分

楼主| 发表于 2024-4-23 16:25:01 | 显示全部楼层
 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。

楼主| 发表于 2024-4-24 10:41:46 | 显示全部楼层
 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。

楼主| 发表于 2024-5-9 18:46:58 | 显示全部楼层
 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？

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

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

 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}

 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}

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