OFFSET
2,1
COMMENTS
This is also the least integer that can be represented as the product of the integers > 1 in two disjoint sets, one having n terms and the other having n-1 terms.
From Jon E. Schoenfield, May 12 2024: (Start)
For n >= 2, let b(n) be the square root of the smallest square that can be expressed as the product of 2*n distinct positive integers; then a(n) >= b(n).
Conjecture: for every n >= 2, a(n) = b(n). (End)
LINKS
Zhao Hui Du, Table of n, a(n) for n = 2..28
Shouwen Wang, Discussion on Chinese BBS on A354457
EXAMPLE
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. (End)
From Zhao Hui Du, May 11 2024: (Start)
For n=9, 133056000 = 1*2*3*9*14*16*20*22*25 = 4*5*6*7*8*10*11*12*15.
For n=10, 2075673600 = 1*2*3*7*15*16*18*20*22*26 = 4*5*6*8*9*10*11*12*13*14. (End)
CROSSREFS
KEYWORD
nonn
AUTHOR
Andy Niedermaier, May 30 2022
EXTENSIONS
a(7)-a(8) from Jinyuan Wang, May 31 2022
a(9)-a(10) from Zhao Hui Du, May 11 2024
a(11)-a(20) from Jon E. Schoenfield, May 11 2024
STATUS
approved