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A127553
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a(n) = Product_{k=1..n} lcm(k,n)/gcd(k,n).
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10
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1, 2, 18, 96, 15000, 6480, 84707280, 41287680, 21427701120, 56700000000, 94121726392108800, 2483144294400, 11159820050604594969600, 24625709514114508800, 620634514500000000000, 359450793240158011392000
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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a(6) = lcm(1,6)/gcd(1,6) * lcm(2,6)/gcd(2,6) * lcm(3,6)/gcd(3,6) * lcm(4,6)/gcd(4,6) * lcm(5,6)/gcd(5,6) * lcm(6,6)/gcd(6,6) = 6/1 * 6/2 * 6/3 * 12/2 * 30/1 * 6/6 = 6480.
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MAPLE
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a:=n->product(ilcm(k, n)/igcd(k, n), k=1..n): seq(a(n), n=1..18); # Emeric Deutsch, Apr 13 2007
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MATHEMATICA
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Table[Product[LCM[k, n]/GCD[k, n], {k, n}], {n, 20}] (* Harvey P. Dale, Jun 10 2017 *)
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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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