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 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). 3
 6, 36, 240, 2520, 30240, 443520, 6652800, 133056000, 2075673600, 58118860800, 1270312243200, 29640619008000, 844757641728000, 25342729251840000, 810967336058880000, 27978373094031360000, 1077167364120207360000, 43086694564808294400000, 1499416970855328645120000 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A001055, A025487, A354697. Sequence in context: A001286 A180119 A181964 * A199422 A049431 A049428 Adjacent sequences: A354454 A354455 A354456 * A354458 A354459 A354460 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

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Last modified September 17 03:10 EDT 2024. Contains 375984 sequences. (Running on oeis4.)