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a(n) = Product_{k=1..n} lcm(k,n)/gcd(k,n).
10

%I #16 Jun 10 2017 09:49:46

%S 1,2,18,96,15000,6480,84707280,41287680,21427701120,56700000000,

%T 94121726392108800,2483144294400,11159820050604594969600,

%U 24625709514114508800,620634514500000000000,359450793240158011392000

%N a(n) = Product_{k=1..n} lcm(k,n)/gcd(k,n).

%H Harvey P. Dale, <a href="/A127553/b127553.txt">Table of n, a(n) for n = 1..238</a>

%F a(n) = A071248(n)/A067911(n). - _R. J. Mathar_, Apr 03 2007

%e 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.

%p A067911 := proc(n) mul( gcd(k,n),k=1..n) ; end: A071248 := proc(n) mul( lcm(k,n),k=1..n) ; end: A127553 := proc(n) A071248(n)/A067911(n) ; end: for n from 1 to 30 do printf("%d, ",A127553(n)) ; od ; # _R. J. Mathar_, Apr 03 2007

%p a:=n->product(ilcm(k,n)/igcd(k,n),k=1..n): seq(a(n),n=1..18); # _Emeric Deutsch_, Apr 13 2007

%t Table[Product[LCM[k,n]/GCD[k,n],{k,n}],{n,20}] (* _Harvey P. Dale_, Jun 10 2017 *)

%Y Cf. A056789.

%K nonn

%O 1,2

%A _Leroy Quet_, Apr 02 2007

%E More terms from _R. J. Mathar_, Apr 03 2007