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！ 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. 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。 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。 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} 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}