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# [求助] 有这样一串数(OEIS找不到)

 n=5 51975        {1,3,21,25,33}        {5,7,9,11,15} 51975        {1,5,15,21,33}        {3,7,9,11,25} 51975        {1,7,9,25,33}        {3,5,11,15,21} 51975        {1,9,11,21,25}        {3,5,7,15,33}

 n=6 1216215        {1,3,15,21,33,39}        {5,7,9,11,13,27} 1216215        {1,5,7,27,33,39}        {3,9,11,13,15,21} 1216215        {1,5,9,21,33,39}        {3,7,11,13,15,27} 1216215        {1,5,11,21,27,39}        {3,7,9,13,15,33} 1216215        {1,5,13,21,27,33}        {3,7,9,11,15,39} 1216215        {1,7,9,15,33,39}        {3,5,11,13,21,27} 1216215        {1,7,11,15,27,39}        {3,5,9,13,21,33} 1216215        {1,7,13,15,27,33}        {3,5,9,11,21,39} 1216215        {1,9,11,15,21,39}        {3,5,7,13,27,33} 1216215        {1,9,13,15,21,33}        {3,5,7,11,27,39} 1216215        {1,11,13,15,21,27}        {3,5,7,9,33,39}

 n=7 42567525        {1,3,9,25,33,39,49}        {5,7,11,13,15,21,27} 42567525        {1,3,11,25,27,39,49}        {5,7,9,13,15,21,33} 42567525        {1,3,13,25,27,33,49}        {5,7,9,11,15,21,39} 42567525        {1,5,9,15,33,39,49}        {3,7,11,13,21,25,27} 42567525        {1,5,11,15,27,39,49}        {3,7,9,13,21,25,33} 42567525        {1,5,13,15,27,33,49}        {3,7,9,11,21,25,39} 42567525        {1,7,9,21,25,33,39}        {3,5,11,13,15,27,49} 42567525        {1,7,11,21,25,27,39}        {3,5,9,13,15,33,49} 42567525        {1,7,13,21,25,27,33}        {3,5,9,11,15,39,49} 42567525        {1,9,11,13,25,27,49}        {3,5,7,15,21,33,39}

### 点评

 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!

楼主| 发表于 2024-5-13 16:24:06 | 显示全部楼层
 本帖最后由 王守恩 于 2024-5-13 18:49 编辑 N=02,           =$$\frac{ 2* 3 }{ 1* 6 }$$ N=03, $$\frac{ 2* 3 }{ 1* 6 }*\frac{3*2}{1}=\frac{ 2* 3* 6 }{ 1* 4* 9 }$$ N=04, $$\frac{ 2* 3* 6 }{ 1* 4* 9 }*\frac{5*4}{3}=\frac{ 2* 4* 5* 6 }{ 1* 3* 8* 10 }$$ , N=05, $$\frac{ 2* 4* 5* 6 }{ 1* 3 *8* 10 }*\frac{7*3}{2}=\frac{ 3* 4* 5* 6* 7 }{ 1* 2* 9* 10* 14 }$$ N=06, $$\frac{ 3* 4* 5* 6* 7 }{ 1* 2* 9* 10* 14 }*\frac{4*3}{1}=\frac{ 2* 5* 6* 7* 8* 9 }{ 1* 3* 4* 12* 14* 15 }=\frac{ 2* 5* 6* 7* 8* 9 }{ 1* 3* 4* 10* 14* 18 }=\frac{ 2* 5* 6* 7* 8* 9 }{ 1* 3* 4* 10* 12* 21 }$$ N=07, $$\frac{ 2* 5* 6* 7* 8* 9 }{ 1* 3* 4* 12* 14* 15 }*\frac{11*4}{3}=\frac{ 3 *4* 5* 6* 7* 8* 22 }{ 1* 2* 9* 10* 11* 14* 16 }$$ N=08, $$\frac{ 3 *4* 5* 6* 7* 8* 22 }{ 1* 2* 9* 10* 11* 14* 16 }*\frac{5*3}{1}=\frac{ 4 *5* 6* 7* 8* 9* 10* 11 }{ 1 *2 *3* 12* 14* 15* 20* 22 }$$ N=09, $$\frac{ 4 *5* 6* 7* 8* 9* 10* 11 }{ 1 *2 *3* 12* 14* 15* 20* 22 }*\frac{5*4}{1}=\frac{ 2*5* 7* 8* 9* 10* 11* 12* 20 }{ 1* 3* 4* 6* 14* 15* 16* 22* 25 }$$ N=10, $$\frac{ 2*5* 7* 8* 9* 10* 11* 12* 20 }{ 1* 3* 4* 6* 14* 15* 16* 22* 25 }*\frac{13*3*2}{5}=\frac{ 2 *6* 7* 8* 9* 10* 11* 12* 13* 20 }{ 1 *3 *4 *5* 14* 15* 16* 18* 22* 26 }$$ N=11, $$\frac{ 2 *6* 7* 8* 9* 10* 11* 12* 13* 20 }{ 1 *3 *4 *5* 14* 15* 16* 18* 22* 26 }*\frac{7*4}{1}=\frac{ 2 *7* 8* 9* 10* 11* 12* 13* 14* 15* 16 }{ 1* 3* 4* 5* 6* 20* 21* 22* 24* 26* 28 }$$ N=12, $$\frac{ 2 *7* 8* 9* 10* 11* 12* 13* 14* 15* 16 }{ 1* 3* 4* 5* 6* 20* 21* 22* 24* 26* 28 }*\frac{17*9}{7}=\frac{ 2 *3* 4* 5* 6* 7* 20* 22* 24* 26* 27* 34 }{ 1* 8* 9* 10* 11* 12* 13* 14* 15* 16* 17* 18 }$$ N=13, $$\frac{ 2 *3* 4* 5* 6* 7* 20* 22* 24* 26* 27* 34 }{ 1* 8* 9* 10* 11* 12* 13* 14* 15* 16* 17* 18 }*\frac{7*5*2}{3}=\frac{ 3* 7* 8* 9* 10* 11* 12* 13* 14* 15* 16* 17* 20 }{ 1* 2* 4* 5* 6* 18* 21* 22* 24* 25* 26* 28* 34 }$$ N=14, $$\frac{ 3* 7* 8* 9* 10* 11* 12* 13* 14* 15* 16* 17* 20 }{ 1* 2* 4* 5* 6* 18* 21* 22* 24* 25* 26* 28* 34 }*\frac{19*3}{2}=\frac{ 2* 7* 9* 10* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20 }{ 1* 3* 4* 5* 6* 8* 21* 22* 25* 26* 27* 28* 34* 38 }$$ N=15, $$\frac{ 2* 7* 9* 10* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20 }{ 1* 3* 4* 5* 6* 8* 21* 22* 25* 26* 27* 28* 34* 38 }*\frac{5*3*2}{1}=\frac{ 4* 5* 9* 10* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21 }{ 1* 2* 3* 6* 7* 8* 22* 24* 25* 26* 27* 30*34*35*38 }$$ N=16, $$\frac{ 4* 5* 9* 10* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21 }{ 1* 2* 3* 6* 7* 8* 22* 24* 25* 26* 27* 30*34*35*38 }*\frac{32}{1}=\frac{ 5* 6* 8* 10* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 24 }{ 1* 2* 3* 4* 7* 9* 22* 25* 26* 27* 28* 30* 32* 34* 38* 40 }$$ N=17,$$\frac{ 5* 6* 8* 10* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 24 }{ 1* 2* 3* 4* 7* 9* 22* 25* 26* 27* 28* 30* 32* 34* 38* 40 }$$*$$\frac{23*3}{2}$$=$$\frac{ 4 *5 *9 *10* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 22* 23* 24 }{ 1* 2* 3* 6* 7* 8* 11* 25* 26* 27* 30* 32* 34* 35* 36* 38* 46 }$$=$$\frac{ 4 *5 *9 *10* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 22* 23* 24 }{ 1* 2* 3* 6* 7* 8* 11* 25* 26* 27* 28* 30* 34* 36* 38*40* 46 }$$=$$\frac{ 4 *5 *9 *10* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 22* 23* 24 }{ 1* 2* 3* 6* 7* 8* 11* 25* 26* 27*28*30*32*34*38* 45*46 }$$ N=18, $$\frac{ 4 *5 *9 *10* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 22* 23* 24 }{ 1* 2* 3* 6* 7* 8* 11* 25* 26* 27* 30* 32* 34* 35* 36* 38* 46 }*\frac{11*7}{2}=\frac{ 2* 3* 4* 5* 6* 7* 8* 10* 26* 27* 30* 33* 34* 35* 38* 42* 44* 46 }{1* 9* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 22* 23* 24* 25* 28 }$$ N=19, $$\frac{ 2* 3* 4* 5* 6* 7* 8* 10* 26* 27* 30* 33* 34* 35* 38* 42* 44* 46 }{1* 9* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 22* 23* 24* 25* 28 }*\frac{5*8}{1}=\frac{ 4* 9* 10* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 22* 23* 24* 25* 28 }{ 1 *2 *3 *5 *6 *7* 8* 26* 27* 30* 32* 33* 34* 35* 38* 42* 44* 46* 50 }=\frac{ 4* 9* 10* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 22* 23* 24* 25* 28 }{ 1 *2 *3 *5 *6 *7* 8* 26* 27* 30* 32* 33* 34* 35* 38* 40* 42* 46* 55 }$$

 n=8 1178512335        {1,3,5,21,33,39,51,57}        {7,9,11,13,15,17,19,27} 1178512335        {1,3,7,15,33,39,51,57}        {5,9,11,13,17,19,21,27} 1178512335        {1,3,11,15,21,39,51,57}        {5,7,9,13,17,19,27,33} 1178512335        {1,3,13,15,21,33,51,57}        {5,7,9,11,17,19,27,39} 1178512335        {1,3,15,17,21,33,39,57}        {5,7,9,11,13,19,27,51} 1178512335        {1,3,15,19,21,33,39,51}        {5,7,9,11,13,17,27,57} 1178512335        {1,5,7,9,33,39,51,57}        {3,11,13,15,17,19,21,27} 1178512335        {1,5,7,11,27,39,51,57}        {3,9,13,15,17,19,21,33} 1178512335        {1,5,7,13,27,33,51,57}        {3,9,11,15,17,19,21,39} 1178512335        {1,5,7,17,27,33,39,57}        {3,9,11,13,15,19,21,51} 1178512335        {1,5,7,19,27,33,39,51}        {3,9,11,13,15,17,21,57} 1178512335        {1,5,9,11,21,39,51,57}        {3,7,13,15,17,19,27,33} 1178512335        {1,5,9,13,21,33,51,57}        {3,7,11,15,17,19,27,39} 1178512335        {1,5,9,17,21,33,39,57}        {3,7,11,13,15,19,27,51} 1178512335        {1,5,9,19,21,33,39,51}        {3,7,11,13,15,17,27,57} 1178512335        {1,5,11,13,21,27,51,57}        {3,7,9,15,17,19,33,39} 1178512335        {1,5,11,17,21,27,39,57}        {3,7,9,13,15,19,33,51} 1178512335        {1,5,11,19,21,27,39,51}        {3,7,9,13,15,17,33,57} 1178512335        {1,5,13,17,21,27,33,57}        {3,7,9,11,15,19,39,51} 1178512335        {1,5,13,19,21,27,33,51}        {3,7,9,11,15,17,39,57} 1178512335        {1,5,17,19,21,27,33,39}        {3,7,9,11,13,15,51,57} 1178512335        {1,7,9,11,15,39,51,57}        {3,5,13,17,19,21,27,33} 1178512335        {1,7,9,13,15,33,51,57}        {3,5,11,17,19,21,27,39} 1178512335        {1,7,9,15,17,33,39,57}        {3,5,11,13,19,21,27,51} 1178512335        {1,7,9,15,19,33,39,51}        {3,5,11,13,17,21,27,57} 1178512335        {1,7,11,13,15,27,51,57}        {3,5,9,17,19,21,33,39} 1178512335        {1,7,11,15,17,27,39,57}        {3,5,9,13,19,21,33,51} 1178512335        {1,7,11,15,19,27,39,51}        {3,5,9,13,17,21,33,57} 1178512335        {1,7,13,15,17,27,33,57}        {3,5,9,11,19,21,39,51} 1178512335        {1,7,13,15,19,27,33,51}        {3,5,9,11,17,21,39,57} 1178512335        {1,7,15,17,19,27,33,39}        {3,5,9,11,13,21,51,57} 1178512335        {1,9,11,13,15,21,51,57}        {3,5,7,17,19,27,33,39} 1178512335        {1,9,11,15,17,21,39,57}        {3,5,7,13,19,27,33,51} 1178512335        {1,9,11,15,19,21,39,51}        {3,5,7,13,17,27,33,57} 1178512335        {1,9,13,15,17,21,33,57}        {3,5,7,11,19,27,39,51} 1178512335        {1,9,13,15,19,21,33,51}        {3,5,7,11,17,27,39,57} 1178512335        {1,9,15,17,19,21,33,39}        {3,5,7,11,13,27,51,57} 1178512335        {1,11,13,15,17,21,27,57}        {3,5,7,9,19,33,39,51} 1178512335        {1,11,13,15,19,21,27,51}        {3,5,7,9,17,33,39,57} 1178512335        {1,11,15,17,19,21,27,39}        {3,5,7,9,13,33,51,57} 1178512335        {1,13,15,17,19,21,27,33}        {3,5,7,9,11,39,51,57}

 n=9 41247931725        {1,3,5,15,33,39,49,51,57}        {7,9,11,13,17,19,21,25,27} 41247931725        {1,3,7,21,25,33,39,51,57}        {5,9,11,13,15,17,19,27,49} 41247931725        {1,3,9,11,25,39,49,51,57}        {5,7,13,15,17,19,21,27,33} 41247931725        {1,3,9,13,25,33,49,51,57}        {5,7,11,15,17,19,21,27,39} 41247931725        {1,3,9,17,25,33,39,49,57}        {5,7,11,13,15,19,21,27,51} 41247931725        {1,3,9,19,25,33,39,49,51}        {5,7,11,13,15,17,21,27,57} 41247931725        {1,3,11,13,25,27,49,51,57}        {5,7,9,15,17,19,21,33,39} 41247931725        {1,3,11,17,25,27,39,49,57}        {5,7,9,13,15,19,21,33,51} 41247931725        {1,3,11,19,25,27,39,49,51}        {5,7,9,13,15,17,21,33,57} 41247931725        {1,3,13,17,25,27,33,49,57}        {5,7,9,11,15,19,21,39,51} 41247931725        {1,3,13,19,25,27,33,49,51}        {5,7,9,11,15,17,21,39,57} 41247931725        {1,3,17,19,25,27,33,39,49}        {5,7,9,11,13,15,21,51,57} 41247931725        {1,5,7,15,21,33,39,51,57}        {3,9,11,13,17,19,25,27,49} 41247931725        {1,5,9,11,15,39,49,51,57}        {3,7,13,17,19,21,25,27,33} 41247931725        {1,5,9,13,15,33,49,51,57}        {3,7,11,17,19,21,25,27,39} 41247931725        {1,5,9,15,17,33,39,49,57}        {3,7,11,13,19,21,25,27,51} 41247931725        {1,5,9,15,19,33,39,49,51}        {3,7,11,13,17,21,25,27,57} 41247931725        {1,5,11,13,15,27,49,51,57}        {3,7,9,17,19,21,25,33,39} 41247931725        {1,5,11,15,17,27,39,49,57}        {3,7,9,13,19,21,25,33,51} 41247931725        {1,5,11,15,19,27,39,49,51}        {3,7,9,13,17,21,25,33,57} 41247931725        {1,5,13,15,17,27,33,49,57}        {3,7,9,11,19,21,25,39,51} 41247931725        {1,5,13,15,19,27,33,49,51}        {3,7,9,11,17,21,25,39,57} 41247931725        {1,5,15,17,19,27,33,39,49}        {3,7,9,11,13,21,25,51,57} 41247931725        {1,7,9,11,21,25,39,51,57}        {3,5,13,15,17,19,27,33,49} 41247931725        {1,7,9,13,21,25,33,51,57}        {3,5,11,15,17,19,27,39,49} 41247931725        {1,7,9,17,21,25,33,39,57}        {3,5,11,13,15,19,27,49,51} 41247931725        {1,7,9,19,21,25,33,39,51}        {3,5,11,13,15,17,27,49,57} 41247931725        {1,7,11,13,21,25,27,51,57}        {3,5,9,15,17,19,33,39,49} 41247931725        {1,7,11,17,21,25,27,39,57}        {3,5,9,13,15,19,33,49,51} 41247931725        {1,7,11,19,21,25,27,39,51}        {3,5,9,13,15,17,33,49,57} 41247931725        {1,7,13,17,21,25,27,33,57}        {3,5,9,11,15,19,39,49,51} 41247931725        {1,7,13,19,21,25,27,33,51}        {3,5,9,11,15,17,39,49,57} 41247931725        {1,7,17,19,21,25,27,33,39}        {3,5,9,11,13,15,49,51,57} 41247931725        {1,9,11,13,17,25,27,49,57}        {3,5,7,15,19,21,33,39,51} 41247931725        {1,9,11,13,19,25,27,49,51}        {3,5,7,15,17,21,33,39,57} 41247931725        {1,9,11,17,19,25,27,39,49}        {3,5,7,13,15,21,33,51,57} 41247931725        {1,9,13,17,19,25,27,33,49}        {3,5,7,11,15,21,39,51,57}

 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

楼主| 发表于 2024-5-14 07:13:35 | 显示全部楼层
 2n个不同正奇数,  n个数的积=n个数的积。我们希望：积是最小的。 根据n=2,3,4,5,6,7,8,9,10的结论,我们能否这样考虑(我们只要这串数)？ (3*5) (3*5) (9*7/5) (5*11/3) (9*13/5) (5*7) (3*17*19/(5*7)) (5*7) (3*5*23/7) ...... 又: 再来两串数, 一并解决了。 数字串(0): 2n个不同整数(最小=0),  n个数的和=n个数的和。我们希望：和是最小的。 数字串(1): 2n个不同整数(最小=1),  n个数的和=n个数的和。我们希望：和是最小的。

 数字串(1): 2n个不同整数(最小=1),  n个数的和=n个数的和。我们希望：和是最小的。 n=2k:  取1-4k 即可 n=2k+1:  取1-4k-1 即可 {5, 11, 18, 28, 39, 53, 68, 86, 105, 127, 150, 176, 203, 233, 264, 298, 333, 371...} $a_n=\ceil[(2*n + 1)*n/2]$

### 评分

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GMT+8, 2024-8-4 15:55 , Processed in 0.209743 second(s), 15 queries .