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A354457
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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).
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3
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6, 36, 240, 2520, 30240, 443520, 6652800, 133056000, 2075673600, 58118860800, 1270312243200, 29640619008000, 844757641728000, 25342729251840000, 810967336058880000, 27978373094031360000, 1077167364120207360000, 43086694564808294400000, 1499416970855328645120000
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OFFSET
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2,1
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COMMENTS
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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.
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)
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LINKS
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EXAMPLE
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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)
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)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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